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Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations/ by Grigorij Kulinich, Svitlana Kushnirenko, Yuliya Mishura.
作者:	Kulinich, Grigorij.
其他作者:	Mishura, Yuliya.
面頁冊數:	XV, 240 p. 4 illus., 2 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Partial Differential Equations. -
電子資源:	https://doi.org/10.1007/978-3-030-41291-3
ISBN:	9783030412913

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
Kulinich, Grigorij.

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations[electronic resource] /by Grigorij Kulinich, Svitlana Kushnirenko, Yuliya Mishura. - 1st ed. 2020. - XV, 240 p. 4 illus., 2 illus. in color.online resource. - Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics,92039-1471 ;. - Bocconi & Springer Series, Mathematics, Statistics, Finance and Economics,6.

Introduction to Unstable Processes and Their Asymptotic Behavior -- Convergence of Unstable Solutions of SDEs to Homogeneous Markov Processes with Discontinuous Transition Density -- Asymptotic Analysis of Equations with Ergodic and Stochastically Unstable Solutions -- Asymptotic Behavior of Integral Functionals of Stochastically Unstable Solutions -- Asymptotic Behavior of Homogeneous Additive Functionals Defined on the Solutions of Itô SDEs with Non-regular Dependence on a Parameter -- Asymptotic Behavior of Homogeneous Additive Functionals of the Solutions to Inhomogeneous Itô SDEs with Non-regular Dependence on a Parameter -- A Selected Facts and Auxiliary Results -- References.

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. .

ISBN: 9783030412913

Standard No.: 10.1007/978-3-030-41291-3doiSubjects--Topical Terms:

671119
Partial Differential Equations.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
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505 0 $a Introduction to Unstable Processes and Their Asymptotic Behavior -- Convergence of Unstable Solutions of SDEs to Homogeneous Markov Processes with Discontinuous Transition Density -- Asymptotic Analysis of Equations with Ergodic and Stochastically Unstable Solutions -- Asymptotic Behavior of Integral Functionals of Stochastically Unstable Solutions -- Asymptotic Behavior of Homogeneous Additive Functionals Defined on the Solutions of Itô SDEs with Non-regular Dependence on a Parameter -- Asymptotic Behavior of Homogeneous Additive Functionals of the Solutions to Inhomogeneous Itô SDEs with Non-regular Dependence on a Parameter -- A Selected Facts and Auxiliary Results -- References.
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