The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential equations and necessary and sufficient conditions ensuring mean-square stability are given. They are applied to typical discretization schemes such as combinations of spectral Galerkin, finite element, Euler-Maruyama, Milstein, Crank-Nicolson, and forward and backward Euler methods. Furthermore, results on the relation to stability properties of corresponding analytical solutions are provided. Simulations of the stochastic heat equation illustrate the theory.
Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.. Keywords: Stochastic modelling; Diffusion process; Stochastic differential equation. ...
TY - JOUR. T1 - Projective integration of expensive multiscale stochastic simulation. AU - Chen, Xiaopeng. AU - Roberts, A. J.. AU - Kevrekidis, Yannis. PY - 2010/12/1. Y1 - 2010/12/1. N2 - Detailed microscale simulation is typically too computationally ex- pensive for the long time simulations necessary to explore macroscale dynamics. Projective integration uses bursts of the microscale simula- tor, on microscale time steps, and then computes an approximation to the system over a macroscale time step by extrapolation. Projective integration has the potential to be an effective method to compute the long time dynamic behaviour of multiscale systems. However, many multiscale systems are significantly in influenced by noise. By a maximum likelihood estimation, we fit a linear stochastic differential equation to short bursts of data. The analytic solution of the linear stochastic differential equation then estimates the solution over a macroscale, projective integration, time step. We explore how ...
Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local ... More. Starting with the construction of stochastic processes, the book introduces Brownian motion and martingales. After proving the Doob-Meyer decomposition, quadratic variation processes and local martingales are discussed. The book proceeds to construct stochastic integrals, prove the Itô formula, derive several important applications of the formula such as the martingale representation theorem and the Burkhölder-Davis-Gundy inequality, and establish the Girsanov theorem on change of measures. Next, attention is focused on stochastic differential equations which arise in modeling physical phenomena, perturbed by random forces. Diffusion processes are solutions of stochastic differential equations and form the main theme of this book. After establishing the existence and uniqueness of strong ...
Several stochastic simulation algorithms (SSAs) have been recently proposed for modelling reaction-diffusion processes in cellular and molecular biology. In this talk, two commonly used SSAs will be studied. The first SSA is an on-lattice model described by the reaction-diffusion master equation. The second SSA is an off-lattice model based on the simulation of Brownian motion of individual molecules and their reactive collisions. The connections between SSAs and the deterministic models (based on reaction-diffusion PDEs) will be presented. I will consider chemical reactions both at a surface and in the bulk. I will show how the microscopic parameters should be chosen to achieve the correct macroscopic reaction rate. This choice is found to depend on which SSA is used. I will also present multiscale algorithms which use models with a different level of detail in different parts of the computational domain ...
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The Gillespie stochastic simulation algorithm (SSA) is the gold standard for simulating state-based stochastic models. If you are a R buff, a SSA novice and want to get quickly up and running stochastic models (in particular ecological models) that are not … Continue reading →
A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the compl A modeling approach to treat noisy engineering systems is presented. We deal with controlled systems that evolve in a continuous-time over finite time intervals, but also in continuous interaction with environments of intrinsic variability. We face the complexity of these systems by introducing a methodology based on Stochastic Differential Equations (SDE) models. We focus on specific type of complexity derived from unpredictable abrupt and/or structural changes. In this paper an approach based on controlled Stochastic Differential Equations with Markovian Switchings (SDEMS) is proposed. Technical conditions for the existence and uniqueness of the solution of these models are provided. We treat with nonlinear SDEMS that does not have closed ...
Arnold, L. (1975): Stochastic Differential Equations New York, John Wiley and Sons.. Bianchi, C., R. Cesari and L. Panattoni (1995): Alternative Estimators of the Cox, Ingersoll and Ross Model of the term Structure of Interest Rates. Roma, Banca dItalia, Temi di Discussione N.326.. Bianchi, C. and E. M. Cleur (1996, forthcomning): Indirect Estimation of Stochastic Differential Equation Models: Some Computational Experiment, Computational Statistics.. Brennan, M.J. and E.S. Schwartz (1979): A Continuous Time Approach to the Pricing of Bonds, Journal of Banking and Finance, 3, 135-155.. Broze, L., O. Scaillet and J.M. Zakoian (1994): Quasi Indirect Inference for Diffusion Processes. Paris: Crest, document de travail No.9511.. Broze, L., O. Scaillet and J.M. Zakoian (1995): Testing for Continuous Time Models of the Short-Term Interest Rate Journal of Empirical Finance, 2, 199-223.. Calzolari, G. (1979): Antithetic Variates to Estimate the Simulation Bias in Non-Linear Models, Economics Letters 4, ...
|p style=text-indent:20px;|When solving linear stochastic differential equations numerically, usually a high order spatial discretisation is used. Balanced truncation (BT) and singular perturbation approximation (SPA) are well-known projection techniques in the deterministic framework which reduce the order of a control system and hence reduce computational complexity. This work considers both methods when the control is replaced by a noise term. We provide theoretical tools such as stochastic concepts for reachability and observability, which are necessary for balancing related model order reduction of linear stochastic differential equations with additive Lévy noise. Moreover, we derive error bounds for both BT and SPA and provide numerical results for a specific example which support the theory.|/p|
1] M.I. Freidlin, Functional Integration and Partial Differential Equations, Princeton University Press, Princeton, 1985. , MR 833742 , Zbl 0568.60057 [2] A. Friedman, Stochastic Differential Equations, Vol. 1, 1975, Academic Press. , Zbl 0323.60056 [3] K. Ichihara, Some Global Properties of Symmetric Diffusion Processes, Publ. RIMS Kyoto Univ., Vol. 14, 1978, pp. 441-486. , MR 509198 , Zbl 0397.60062 [4] R.Z. Khasminkii, Ergodic Properties of Recurrent Diffusion Processes and Stabilization of the Solution of the Cauchy Problem for Parabolic Equations, Proc. Theory and Appl., Vol. 5, 1960, pp. 179-196. , MR 133871 , Zbl 0106.12001 [5] R.Z. Khasminskii, On the Averaging Principle for Stochastic Differential Equations, Kybernetika, Academia, Praha, Vol. 4, 1968, pp. 260-279 (Russian). , MR 260052 , Zbl 0231.60045 [6] M.A. Pinsky and R.G. Pinsky, Transience and Recurrence for Diffusions in Random Temporal Environments, Annals of Probability (to appear). [7] R.G. Pinsky, Transience and Recurrence ...
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Author summary Genetically identical cells, even when they are exposed to the same environmental conditions, display incredible diversity. Gene expression noise is attributed to be a key source of this phenotypic diversity. Transcriptional dynamics is a dominant source of expression noise. Although scores of theoretical and experimental studies have explored how noise is regulated at the level of transcription, most of them focus on the gene specific, cis regulatory elements, such as the number of transcription factor (TF) binding sites, their binding strength, etc. However, how the global properties of transcription, such as the limited availability of TFs impact noise in gene expression remains rather elusive. Here we build a theoretical model that incorporates the effect of limiting TF pool on gene expression noise. We find that competition between genes for TFs leads to enhanced variability in mRNA copy number across an isogenic population. Moreover, for gene copies sharing TFs with other competitor
Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential equations. A complex nonlinear nonstationary stochastic system of differential equations are decomposed into nonlinear systems of stochastic perturbed and unperturbed differential equations. Using this type of decomposition, the fundamental properties of
In this paper, we develop a stochastic differential equation model to simulate the movement of a social/subsocial spider species, |em|Anelosimus studiosus|/em|, during prey capture using experimental data collected in a structured environment. In a subsocial species, females and their maturing offspring share a web and cooperate in web maintenance and prey capture. Furthermore, observations indicate these colonies change their positioning throughout the day, clustered during certain times of the day while spaced out at other times. One key question was whether or not the spiders spaced out ``optimally to cooperate in prey capture. In this paper, we first show the derivation of the model where experimental data is used to determine key parameters within the model. We then use this model to test the success of prey capture under a variety of different spatial configurations for varying colony sizes to determine the best spatial configuration for prey capture.
Background. The chemical master equation is the fundamental equation of stochastic chemical kinetics. This differential-difference equation describes temporal evolution of the probability density function for states of a chemical system. A state of the system, usually encoded as a vector, represents the number of entities or copy numbers of interacting species, which are changing according to a list of possible reactions. It is often the case, especially when the state vector is high-dimensional, that the number of possible states the system may occupy is too large to be handled computationally. One way to get around this problem is to consider only those states that are associated with probabilities that are greater than a certain threshold level. Results. We introduce an algorithm that significantly reduces computational resources and is especially powerful when dealing with multi-modal distributions. The algorithm is built according to two key principles. Firstly, when performing time ...
Accurate modeling of reaction kinetics is important to understand how biological cells work. Spatially well-mixed reaction dynamics can be modeled by the chemical master equation (CME, see formula 2), an infinite set of ordinary differential equations, which is, in general, too complex to be solved analytically. There are accurate numerical simulation schemes for solving the CME indirectly, like Gillespies stochastic simulation algorithm (FN:D. T. Gillespie. Exact Stochastic Simulation of Coupled Chemical Reactions. Journal of Physical Chemistry, 81[25]:2340-2361, 1977.). For many relevant realistic settings, however, even our high-performance computers fail to create reliable statistics within an acceptable amount of time. This is the motivation to reduce the model complexity by considering approximative mathematical formulations of the cellular dynamics. Especially multiscale reaction systems, which often appear in real-world applications, are in the focus of our investigations because they ...
An old and important problem in the field of nonlinear time-series analysis entails the distinction between chaotic and stochastic dynamics. Recently, e-recurrence networks have been proposed as a tool to analyse the structural properties of a time series. In this paper, we propose the applicability of local and global e-recurrence network measures to distinguish between chaotic and stochastic dynamics using paradigmatic model systems such as the Lorenz system, and the chaotic and hyper-chaotic Rossler system. We also demonstrate the effect of increasing levels of noise on these network measures and provide a real-world application of analysing electroencephalographic data comprising epileptic seizures. Our results show that both local and global e-recurrence network measures are sensitive to the presence of unstable periodic orbits and other structural features associated with chaotic dynamics that are otherwise absent in stochastic dynamics. These network measures are still robust at high ...
A balanced approach to probability, statistics, stochastic models, and stochastic differential equations with special emphasis on engineering applications. Random variables, probability distributions, Monte Carlo simulations models, statistical inference theory, design of engineering experiments, reliability and risk assessment, fitting data to probability distributions, ANOVA, stochastic processes, Brownian motion, white noise, random walk, colored noise processes. Differential equations subject to random initial conditions, random forcing functions, and random parameters. Partial differential equations subject to stochastic boundary conditions. New techniques for non-linear differential equations. Computer simulation with MAPLE and other symbolic algebra software. 0520. Introduction to Bioengineering (3 s.h.) ...
InCharge,author1=Christoph Hauert}} {{TOCright}} Stochastic differential equations (SDE) provide a general framework to describe the evolutionary dynamics of an arbitrary number of strategic types \(d\) in finite populations, which results in demographic noise, as well as to incorporate mutations. For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, \(\mu\), are not too small compared to the inverse population size \(1/N\). This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For \(\mu N\ll1\) this limits the use of SDEs, but in this case well established alternative approximations are available based on time scale separation. The ...
InCharge,author1=Christoph Hauert}} {{TOCright}} Stochastic differential equations (SDE) provide a general framework to describe the evolutionary dynamics of an arbitrary number of strategic types \(d\) in finite populations, which results in demographic noise, as well as to incorporate mutations. For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, \(\mu\), are not too small compared to the inverse population size \(1/N\). This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For \(\mu N\ll1\) this limits the use of SDEs, but in this case well established alternative approximations are available based on time scale separation. The ...
The inhomogeneous stochastic simulation algorithm (ISSA) is a fundamental method for spatial stochastic simulation. However, when diffusion events occur more frequently than reaction events, simulating the diffusion events by ISSA is quite costly. To reduce this cost, we propose to use the time dependent propensity function in each step. In this way we can avoid simulating individual diffusion events, and use the time interval between two adjacent reaction events as the simulation stepsize. We demonstrate that the new algorithm can achieve orders of magnitude efficiency gains over widely-used exact algorithms, scales well with increasing grid resolution, and maintains a high level of accuracy.. ...
While the birth-death model is, in itself, inappropriate for representing intracellular bacteria (§1), it has provided a useful foundation for the birth-death-survival model considered here. In the 1960s, there was considerable academic interest in the mathematics of the simple birth-death model, involving stochastic differential equations [14,15] and generating functions [48]. However, very few experimental studies have actually made use of these results, despite a thorough account [23] crediting their ability in representing data for a variety of diseases. That paper [23] and methods therein are however not without their critics. It is claimed [5] that while the overall picture provided by the basic birth-death model corresponds remarkably well to what is found in practice, the underlying interpretations are flawed and there is no experimental evidence to suggest any form of stochastic mechanism in the infection dynamics. However, this is later refuted in an in vivo study [40] (in which ...
TY - ABST. T1 - Stochastic simulation model for spatial-temporal development of a fungal plant disease spread by wind. AU - Østergård, Hanne. PY - 2003. Y1 - 2003. KW - 9-B risiko. M3 - Conference abstract for conference. T2 - Dina workshop on dispersal models with agricultural applications. Y2 - 1 January 2003. ER - ...
Real-time in situ operation of bio/chemical sensors assumes detection of chemical substances or biological specimens in samples of complex composition. Since sensor selectivity cannot be ideal, adsorption of particles other than target particles inevitably occur on the sensing surface. That affects the sensor response and its intrinsic fluctuations which are caused by stochastic fluctuations of the numbers of adsorbed particles of all the adsorbing substances. In microfluidic sensors, such response fluctuations are a result of coupled adsorption, desorption and mass transfer (convection and diffusion) processes of analyte particles. Analysis of these fluctuations is important because they constitute the adsorption-desorption noise, which limits the sensing performance. In this work we perform the analysis of fluctuations by using a stochastic model of sensor response after the steady state is reached, in the case of two-analyte adsorption, considering mass transfer processes. The resul...ts ...
This page collects some information about stochastic systems courses offered at Caltech. This page was prepared in preparation for a faculty discussion on the current stochastic systems sequence (ACM/EE 116, ACM 216, ACM 217/EE 164). == Introduction == === Background === The current sequence of courses (ACM/EE 116, ACM 216, ACM 217/EE 164) were first offered in the 2005-06 academic year following discussions between Emmanuel Candes, Babak Hassibi, Jerry Marsden, Richard Murray and Houman Ohwadi about how to integrate some of the course offerings in ACM and EE, with an eye toward applications in CDS. EE 162 (Random Processes for Communication and Signal Processing) was eliminated and replaced by ACM/EE 116. There are three drivers for evaluating the course sequence at this time: * Its been a while since we set this up and it would be good to get together and see what we think about how its been going. * CDS is about to require ACM 116 as part of its PhD requirements (in place of CDS 140b) and ...
Methods to implement stochastic simulations on the graphics processing unit (GPU) have been developed. These algorithms are used in a simulation of microassembly and nanoassembly with optical tweezers, but are also directly compatible with simulations of a wide variety of assembly techniques using either electrophoretic, magnetic, or other trapping techniques. Significant speedup is possible for stochastic particle simulations when using the GPU, included in most personal computers (PCs), rather than the central processing unit (CPU) that handles most calculations. However, a careful analysis of the accuracy and precision when using the GPU in stochastic simulations is lacking and is addressed here. A stochastic simulation for spherical particles has been developed and mapped onto stages of the GPU hardware that provide the best performance. The results from the CPU and GPU implementation are then compared with each other and with well-established theory. The error in the mean ensemble energy ...
Research and Markets: Stochastic Simulation and Applications in Finance with MATLAB: DUBLIN, Ireland--(BUSINESS WIRE)--January 23, 2009-- Research and Markets (http://www.researchandmarkets.com/research/40d9cd/stochastic_simulat) has announced the addition of John Wiley and Sons Ltds new report &Stochastic Simulation and Applications in Finance with MATLAB Programs& to their offering. Stochastic Simulation and Applications in Finance with MATLAB Programs explains the …
The workshop will focus on Rough Path Analysis and its rapidly growing applications in Applied Stochastic Analysis, ranging from the resolution of ill-posed stochastic partial differential equations to new ways of handling highdimensional data. ...
The development of plants impresses us with the well-orchestrated formation of tissues and structures throughout the lifetime of the organism, despite its constituents being inherently stochastic. At first glance the prevalent noise on the molecular level seems hard to reconcile with the robustness and reproducibility of development. How is stochastic variability overcome during development and developmental decision-making? When is stochasticity employed to generate patterns? How can stochastic events drive a process? How do lower level stochastic fluctuations affect development at more global levels? Stochastic variability is prevalent whenever low molecule numbers and/or small system sizes are involved. Especially during development a few cells are at the foundation of a growing organ, and the stochastic dynamics of regulatory molecules drive spatiotemporal specification of structures to be. Stochasticity is emerging as an important factor in the regulation of diverse plant developmental
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Stochastic analysis of steady-state two-phase (water and oil) flow in heterogeneous porous media is performed using the perturbation theory and spectral representation techniques. The governing equations describing the flow are coupled and nonlinear. The key stochastic input variables are intrinsic permeability,k, and the soil and fluid dependent retention parameter, г. Three different stochastic combinations of these two imput parameters were considered. The perturbation/spectral analysis was used to develop closed-form expressions that describe stochastic variability of key output processes, such as capillary and individual phase pressures and specific discharges. The analysis also included the estimation of the effective flow properties. The impact of the spatial variability ofk and г on the variances of pressures, effective conductivities, and specific discharges was examined.
Stochastic Analysis of Neural Spike Count Dependencies [Elektronische Ressource] / Arno Onken. Betreuer: Klaus Obermayer : Technische Universitat Berlin¨Stochastic Analysisof Neural Spike Count Dependenciesvorgelegt vonDiplom-InformatikerArno Onkenaus AurichVon der Fakultat IV - Elektrotechnik und Informatik¨der Technischen Universitat Berlin¨zur Erlangung des akademischen GradesDoktor der NaturwissenschaftenDr. rer. nat.genehmigte DissertationPromotionsausschuss:Vorsitzender: Prof. Dr. Klaus-Robert Mu¨llerBerichter:
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Gene expression within cells is known to fluctuate stochastically in time. However, the origins of gene expression noise remain incompletely understood. The bacterial cell cycle has been suggested as one source, involving chromosome replication, exponential volume growth, and various other changes in cellular composition. Elucidating how these factors give rise to expression variations is important to models of cellular homeostasis, fidelity of signal transmission, and cell-fate decisions. Using single-cell time-lapse microscopy, we measured cellular growth as well as fluctuations in the expression rate of a fluorescent protein and its concentration. We found that, within the population, the mean expression rate doubles throughout the cell cycle with a characteristic cell cycle phase dependent shape which is different for slow and fast growth rates. At low growth rate, we find the mean expression rate was initially flat, and then rose approximately linearly by a factor two until the end of the cell
Generation and filtering of gene expression noise by the bacterial cell cycle. . Biblioteca virtual para leer y descargar libros, documentos, trabajos y tesis universitarias en PDF. Material universiario, documentación y tareas realizadas por universitarios en nuestra biblioteca. Para descargar gratis y para leer online.
We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial
Finden Sie alle Bücher von Moisés Santillán - Chemical Kinetics, Stochastic Processes, and Irreversible Thermodynamics. Bei der Büchersuchmaschine eurobuch.de können Sie antiquarische und Neubücher VERGLEICHEN UND SOFORT zum Bestpreis bestellen. 9783319066882
Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics (predicting the motions of planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. Before the advent of modern ...
Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system ẋ(t) = f(x(t)) into the Itô form dx(t) = f(x(t))dt + g(x(t))dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with probability one that of the associated stochastic differential equation does not.. ...
Modeling and simulation of biochemical networks faces numerous challenges as biochemical networks are discovered with increased complexity and unknown mechanisms. With improvement in experimental techniques, biologists are able to quantify genes and proteins and their dynamics in a single cell, which calls for quantitative stochastic models, or numerical models based on probability distributions, for gene and protein networks at cellular levels that match well with the data and account for randomness. This dissertation studies a stochastic model in space and time of a bacteriums life cycle- Caulobacter. A two-dimensional model based on a natural pattern mechanism is investigated to illustrate the changes in space and time of a key protein population. However, stochastic simulations are often complicated by the expensive computational cost for large and sophisticated biochemical networks. The hybrid stochastic simulation algorithm is a combination of traditional deterministic models, or ...
All populations fluctuate stochastically, creating a risk of extinction that does not exist in deterministic models, with fundamental consequences for both pure and applied ecology. This book provides an introduction to stochastic population dynamics, combining classical background material with a variety of modern approaches, including previously unpublished results by the authors, illustrated with examples from bird and mammal populations, and insect communities. Demographic and environmental stochasticity are introduced with statistical methods for estimating them from field data. The long-run growth rate of a population is explained and extended to include age structure with both demographic and environmental stochasticity. Diffusion approximations facilitate the analysis of extinction dynamics and the duration of the final decline. Methods are developed for estimating delayed density dependence from population time series using life history data. Metapopulation viability and the spatial scale of
Randomness is an important component of modeling complex phenomena in biological, chemical, physical, and engineering systems. Based on many years teaching this material, Jinqiao Duan develops a modern approach to the fundamental theory and application of stochastic dynamical systems for applied mathematicians and quantitative engineers and scientists. The highlight is the staged development of invariant stochastic structures that underpin much of our understanding of nonlinear stochastic systems and associated properties such as escape times. The book ranges from classic Brownian motion to noise generated by α-stable Levy flights. A. J. Roberts, University of Adelaide. This book provides a beautiful concise introduction to the flourishing field of stochastic dynamical systems, successfully integrating the exposition of important technical concepts with illustrative and insightful examples and interesting remarks regarding the simulation of such systems. Both presentation style and content ...
This book presents the proceedings from the International Conference held in Halifax, NS in July 1997. Funded by The Fields Institute and Le Centre de Recherches Mathématiques, the conference was held in honor of the retirement of Professors Lynn Erbe and Herb I. Freedman (University of Alberta). Featured topics include ordinary, partial, functional, and stochastic differential equations and their applications to biology, epidemiology, neurobiology, physiology and other related areas ...
By a novel approach, we get some explicit criteria for the mean square exponential stability of linear stochastic differential equations with distributed delays. Stability criteria presented in this...
Expansions in Generalized Eigenfunctions of the Weighted Laplacian on Star-shaped Networks -- Diffusion Equations with Finite Speed of Propagation -- Subordinated Multiparameter Groups of Linear Operators: Properties via the Transference Principle -- An Integral Equation in AeroElasticity -- Eigenvalue Asymptotics Under a Non-dissipative Eigenvalue Dependent Boundary Condition for Second-order Elliptic Operators -- Feynman-Kac Formulas, Backward Stochastic Differential Equations and Markov Processes -- Generation of Cosine Families on L p (0,1) by Elliptic Operators with Robin Boundary Conditions -- Global Smooth Solutions to a Fourth-order Quasilinear Fractional Evolution Equation -- Positivity Property of Solutions of Some Quasilinear Elliptic Inequalities -- On a Stochastic Parabolic Integral Equation -- Resolvent Estimates for a Perturbed Oseen Problem -- Abstract Delay Equations Inspired by Population Dynamics -- Weak Stability for Orbits of C 0-semigroups on Banach Spaces -- Contraction ...
This article is concerned with the fluctuation analysis and the stability properties of a class of one-dimensional Riccati diffusions. This class of Riccati diffusion is quite general, and arises, for example, in data assimilation applications, and more particularly in ensemble (Kalman-type) filtering theory. These one-dimensional stochastic differential equations exhibit a quadratic drift function and a non-Lipschitz continuous diffusion function. We present a novel approach, combining tangent process techniques, Feynman-Kac path integration, and exponential change of measures, to derive sharp exponential decays to equilibrium. We also provide uniform estimates with respect to the time horizon, quantifying with some precision the fluctuations of these diffusions around a limiting deterministic Riccati differential equation. These results provide a stronger and almost sure version of the conventional central limit theorem. We illustrate these results in the context of ensemble Kalman-Bucy filtering. In
砂漠の洪水を灌漑用水に変える --ヨルダンの乾燥地で数理的最適戦略によるプロトタイプを運用--. 京都大学プレスリリース. 2018-03-08.Operation of reservoirs is a fundamental issue in water resource management. We herein investigate well-posedness of an optimal control problem for irrigation water intake from a reservoir in an irrigation scheme, the water dynamics of which is modeled with stochastic differential equations. A prototype irrigation scheme is being developed in an arid region to harvest flash floods as a source of water. The Hamilton-Jacobi-Bellman (HJB) equation governing the value function is analyzed in the framework of viscosity solutions. The uniqueness of the value function, which is a viscosity solution to the HJB equation, is demonstrated with a mathematical proof of a comparison theorem. It is also shown that there exists such a viscosity solution. Then, an approximate value function is obtained as a numerical solution to the HJB ...
Title: Particle representations for SPDEs and strict positivity of solutions Abstract: Stochastic partial differential equations arise naturally as limits of finite systems of interacting particles. For a variety of purposes, it is useful to keep the particles in the limit obtaining an infinite exchangeable system of stochastic differential equations. The corresponding de Finetti measure then gives the solution of the SPDE. These representations frequently simplify existence, uniqueness and convergence results. The support properties of the measure-valued solution can be studied using Girsanov change of measure techniques. The ideas will be illustrated by a model of asset prices set by an infinite system of competing traders. These latter results are joint work with Dan Crisan and Yoonjung Lee. ...