Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations
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Beschreibung
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.
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.
Of great interest for practitioners and researchers who apply stochastic models to describe phenomena of instability Contains results on the weak convergence of a wide class of functionals of SDE solutions Includes a range of examples illustrating statements about weak convergence
Autor*in
Grigorij Kulinich
Themen in »Asymptotic Analysis of Unstable Solutions of Stochastic Differential Equations«
Stochastic differential equation Asymptotic behavior of solution Nonregular dependence on parameter Unstable solution Diffusion process ordinary differential equations partial differential equations
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“The book will be of interest to anybody working in stochastic analysis and its applications, from master and PhD students to professional researchers. Applied scientists can also benefit from this book by seeing efficient methods to deal with unstable processes.” (Jordan M. Stoyanov, zbMATH 1456.60002, 2021)
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