Asymptotic Analysis for Functional Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Analysis for Functional Stochastic Differential Equations write by Jianhai Bao. This book was released on 2016-11-19. Asymptotic Analysis for Functional Stochastic Differential Equations available in PDF, EPUB and Kindle. 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.
Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations write by Grigorij Kulinich. This book was released on 2020-04-29. Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations available in PDF, EPUB and Kindle. 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.
Two-Scale Stochastic Systems
Two-Scale Stochastic Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Two-Scale Stochastic Systems write by Yuri Kabanov. This book was released on 2013-04-17. Two-Scale Stochastic Systems available in PDF, EPUB and Kindle. Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.Two-scale systems described by singularly perturbed SDEs have been the subject of ample literature. However, this new monograph develops subjects that were rarely addressed and could be given the collective description "Stochastic Tikhonov-Levinson theory and its applications." The book provides a mathematical apparatus designed to analyze the dynamic behaviour of a randomly perturbed system with fast and slow variables. In contrast to the deterministic Tikhonov-Levinson theory, the basic model is described in a more realistic way by stochastic differential equations. This leads to a number of new theoretical questions but simultaneously allows us to treat in a unified way a surprisingly wide spectrum of applications like fast modulations, approximate filtering, and stochastic approximation.
Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations
Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations write by Anatoli? Mikha?lovich Samo?lenko. This book was released on 2011. Qualitative and Asymptotic Analysis of Differential Equations with Random Perturbations available in PDF, EPUB and Kindle. 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.
Asymptotic Analysis of Differential Equations
Asymptotic Analysis of Differential Equations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Asymptotic Analysis of Differential Equations write by R. B. White. This book was released on 2010. Asymptotic Analysis of Differential Equations available in PDF, EPUB and Kindle. "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.
