Asymptotic Methods in the Theory of Stochastic Differential Equations
Author: Anatoliĭ Vladimirovich Skorokhod
Publisher: Amer Mathematical Society
Published: 1989
Total Pages: 339
ISBN-13: 9780821845318
DOWNLOAD EBOOK →Author: Anatoliĭ Vladimirovich Skorokhod
Publisher: Amer Mathematical Society
Published: 1989
Total Pages: 339
ISBN-13: 9780821845318
DOWNLOAD EBOOK →Author: A. V. Skorokhod
Publisher: American Mathematical Soc.
Published: 2009-01-07
Total Pages: 339
ISBN-13: 9780821846865
DOWNLOAD EBOOK →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.
Author: A. V. Skorokhod
Publisher: American Mathematical Soc.
Published: 2009-01-07
Total Pages: 362
ISBN-13: 9780821898253
DOWNLOAD EBOOK →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
Author: Grigorij Kulinich
Publisher: Springer Nature
Published: 2020-04-29
Total Pages: 240
ISBN-13: 3030412911
DOWNLOAD EBOOK →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.
Author: Anatoliy M Samoilenko
Publisher: World Scientific
Published: 2011-06-07
Total Pages: 323
ISBN-13: 981446239X
DOWNLOAD EBOOK →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 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.
Author: White Roscoe B
Publisher: World Scientific
Published: 2010-08-16
Total Pages: 432
ISBN-13: 1911298593
DOWNLOAD EBOOK →The book gives the practical means of finding asymptotic solutions to differential equations, and relates WKB methods, integral solutions, Kruskal-Newton diagrams, and boundary layer theory to one another. The construction of integral solutions and analytic continuation are used in conjunction with the asymptotic analysis, to show the interrelatedness of these methods. Some of the functions of classical analysis are used as examples, to provide an introduction to their analytic and asymptotic properties, and to give derivations of some of the important identities satisfied by them. The emphasis is on the various techniques of analysis: obtaining asymptotic limits, connecting different asymptotic solutions, and obtaining integral representation.
Author: Stepan Fedorovič Feščenko
Publisher:
Published: 1967
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOK →Author: Jianhai Bao
Publisher: Springer
Published: 2016-11-19
Total Pages: 159
ISBN-13: 3319469797
DOWNLOAD EBOOK →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.
Author: Johan Grasman
Publisher: Springer Science & Business Media
Published: 1999-03-08
Total Pages: 242
ISBN-13: 9783540644354
DOWNLOAD EBOOK →Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.
Author: Stepan Fedorovich Feshchenko
Publisher:
Published: 1967
Total Pages: 268
ISBN-13:
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