Asymptotic analysis of unstable solutions of stochastic differential equations
- 作者： Kulinich, Grigorij, author.
- 其他作者：
- 其他題名：
- Bocconi & Springer series, mathematics, statistics, finance and economics ;
- 出版： Cham : Springer International Publishing :Imprint: Springer
- 叢書名： Bocconi & Springer series, mathematics, statistics, finance and economics,volume 9
- 主題： Stochastic differential equations. , Probability Theory and Stochastic Processes. , Dynamical Systems and Ergodic Theory. , Ordinary Differential Equations. , Functional Analysis. , Partial Differential Equations.
- ISBN： 9783030412913 (electronic bk.) 、 9783030412906 (paper)
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FIND@SFXID:
CGU
- 資料類型: 電子書
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讀者標籤：
- 系統號： 005483022 | 機讀編目格式
館藏資訊
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.