Download or read book Asymptotic Methods in the Theory of Stochastic Differential Equations written by Anatoliĭ Vladimirovich Skorokhod and published by Amer Mathematical Society. This book was released on 1989 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Stochastic Differential Equations written by A. V. Skorokhod and published by American Mathematical Soc.. This book was released on 2009-01-07 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the foremost Soviet experts in the field, this book is intended for specialists in the theory of random processes and its applications. The author's 1982 monograph on stochastic differential equations, written with Iosif Ilich Gikhman, did not include a number of topics important to applications. The present work begins to fill this gap by investigating the asymptotic behavior of stochastic differential equations. The main topics are ergodic theory for Markov processes and for solutions of stochastic differential equations, stochastic differential equations containing a small parameter, and stability theory for solutions of systems of stochastic differential equations.
Download or read book Asymptotic Methods in the Theory of Stochastic Differential Equations written by A. V. Skorokhod and published by American Mathematical Soc.. This book was released on 2009-01-07 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ergodic theorems: General ergodic theorems Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations Ergodic theorems for one-dimensional stochastic equations Ergodic theorems for solutions of stochastic equations in $R^d$ Asymptotic behavior of systems of stochastic equations containing a small parameter: Equations with a small right-hand side Processes with rapid switching Averaging over variables for systems of stochastic differential equations Stability. Linear systems: Stability of sample paths of homogeneous Markov processes Linear equations in $R^d$ and the stochastic semigroups connected with them. Stability Stability of solutions of stochastic differential equations Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability: Linear equations with bounded coefficients Strong stochastic semigroups with second moments Stability Bibliography
Download or read book Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations written by Grigorij Kulinich and published by Springer Nature. This book was released on 2020-04-29 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to unstable solutions of stochastic differential equations (SDEs). Despite the huge interest in the theory of SDEs, this book is the first to present a systematic study of the instability and asymptotic behavior of the corresponding unstable stochastic systems. The limit theorems contained in the book are not merely of purely mathematical value; rather, they also have practical value. Instability or violations of stability are noted in many phenomena, and the authors attempt to apply mathematical and stochastic methods to deal with them. The main goals include exploration of Brownian motion in environments with anomalies and study of the motion of the Brownian particle in layered media. A fairly wide class of continuous Markov processes is obtained in the limit. It includes Markov processes with discontinuous transition densities, processes that are not solutions of any Itô's SDEs, and the Bessel diffusion process. The book is self-contained, with presentation of definitions and auxiliary results in an Appendix. It will be of value for specialists in stochastic analysis and SDEs, as well as for researchers in other fields who deal with unstable systems and practitioners who apply stochastic models to describe phenomena of instability.
Download or read book Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations written by Anatoli? Mikha?lovich Samo?lenko and published by World Scientific. This book was released on 2011 with total page 323 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations with random perturbations are the mathematical models of real-world processes that cannot be described via deterministic laws, and their evolution depends on the random factors. The modern theory of differential equations with random perturbations is on the edge of two mathematical disciplines: random processes and ordinary differential equations. Consequently, the sources of these methods come both from the theory of random processes and from the classic theory of differential equations. This work focuses on the approach to stochastic equations from the perspective of ordinary differential equations. For this purpose, both asymptotic and qualitative methods which appeared in the classical theory of differential equations and nonlinear mechanics are developed.
Download or read book Asymptotic Analysis of Differential Equations written by R. B. White and published by World Scientific. This book was released on 2010 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Download or read book Asymptotic Methods in the Theory of Linear Differential Equations written by Stepan Fedorovič Feščenko and published by . This book was released on 1967 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Analysis for Functional Stochastic Differential Equations written by Jianhai Bao and published by Springer. This book was released on 2016-11-19 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief treats dynamical systems that involve delays and random disturbances. The study is motivated by a wide variety of systems in real life in which random noise has to be taken into consideration and the effect of delays cannot be ignored. Concentrating on such systems that are described by functional stochastic differential equations, this work focuses on the study of large time behavior, in particular, ergodicity.This brief is written for probabilists, applied mathematicians, engineers, and scientists who need to use delay systems and functional stochastic differential equations in their work. Selected topics from the brief can also be used in a graduate level topics course in probability and stochastic processes.
Download or read book Asymptotic Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Download or read book Asymptotic Methods in the Theory of Non linear Oscillations written by Nikolaĭ Nikolaevich Bogoli︠u︡bov and published by CRC Press. This book was released on 1961 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Asymptotic Methods in the Theory of Linear Differential Equations written by Stepan Fedorovich Feshchenko and published by . This book was released on 1967 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Introduction to Asymptotic Methods written by David Y. Gao and published by CRC Press. This book was released on 2006-05-03 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m
Download or read book Statistical Methods for Stochastic Differential Equations written by Mathieu Kessler and published by CRC Press. This book was released on 2012-05-17 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: The seventh volume in the SemStat series, Statistical Methods for Stochastic Differential Equations presents current research trends and recent developments in statistical methods for stochastic differential equations. Written to be accessible to both new students and seasoned researchers, each self-contained chapter starts with introductions to th
Download or read book Stochastic Differential Equations written by Ludwig Arnold and published by Wiley-Interscience. This book was released on 1974-04-23 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of probability theory; Markov processes and diffusion processes; Wiener process and white noise; Stochastic integrals; The stochastic integral as a stochastic process, stochastic differentials; Stochastic differential equations, existence and uniqueness of solutions; Properties of the solutions of stochastic differential equations; Linear stochastic differentials equations; The solutions of stochastic differentail equations as Markov and diffusion processes; Questions of modeling and approximation; Stability of stochastic dynamic systems; Optimal filtering of a disturbed signal; Optimal control of stochastic dynamic systems.
Download or read book Stochastic Differential Equations in Infinite Dimensions written by Leszek Gawarecki and published by Springer Science & Business Media. This book was released on 2010-11-29 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: The systematic study of existence, uniqueness, and properties of solutions to stochastic differential equations in infinite dimensions arising from practical problems characterizes this volume that is intended for graduate students and for pure and applied mathematicians, physicists, engineers, professionals working with mathematical models of finance. Major methods include compactness, coercivity, monotonicity, in a variety of set-ups. The authors emphasize the fundamental work of Gikhman and Skorokhod on the existence and uniqueness of solutions to stochastic differential equations and present its extension to infinite dimension. They also generalize the work of Khasminskii on stability and stationary distributions of solutions. New results, applications, and examples of stochastic partial differential equations are included. This clear and detailed presentation gives the basics of the infinite dimensional version of the classic books of Gikhman and Skorokhod and of Khasminskii in one concise volume that covers the main topics in infinite dimensional stochastic PDE’s. By appropriate selection of material, the volume can be adapted for a 1- or 2-semester course, and can prepare the reader for research in this rapidly expanding area.
Download or read book Applied Stochastic Differential Equations written by Simo Särkkä and published by Cambridge University Press. This book was released on 2019-05-02 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: With this hands-on introduction readers will learn what SDEs are all about and how they should use them in practice.
Download or read book Markov Processes and Differential Equations written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 1996-03-28 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt: Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations. Due to the close connection between the second order differential operators with a non-negative characteristic form on the one hand and Markov processes on the other, many problems in PDE's can be reformulated as problems for corresponding stochastic processes and vice versa. In the present book four classes of problems are considered: - the Dirichlet problem with a small parameter in higher derivatives for differential equations and systems - the averaging principle for stochastic processes and PDE's - homogenization in PDE's and in stochastic processes - wave front propagation for semilinear differential equations and systems. From the probabilistic point of view, the first two topics concern random perturbations of dynamical systems. The third topic, homog- enization, is a natural problem for stochastic processes as well as for PDE's. Wave fronts in semilinear PDE's are interesting examples of pattern formation in reaction-diffusion equations. The text presents new results in probability theory and their applica- tion to the above problems. Various examples help the reader to understand the effects. Prerequisites are knowledge in probability theory and in partial differential equations.
