Stochastic Stability of Differential Equations in Abstract Spaces (London Mathematical Society Lecture Note Series, Series Number 453)

The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier-Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology.;Preliminaries -- Stability of linear stochastic differential equations -- Stability of non linear stochastic differential equations -- Stability of stochastic functional differential equations -- Some applications related to stochastic stability. "The stability of stochastic differential equations in abstract, mainly Hilbert, spaces receives a unified treatment in this self-contained book. It covers basic theory as well as computational techniques for handling the stochastic stability of systems from mathematical, physical and biological problems. Its core material is divided into three parts devoted respectively to the stochastic stability of linear systems, non-linear systems, and time-delay systems. The focus is on stability of stochastic dynamical processes affected by white noise, which are described by partial differential equations such as the Navier–Stokes equations. A range of mathematicians and scientists, including those involved in numerical computation, will find this book useful. It is also ideal for engineers working on stochastic systems and their control, and researchers in mathematical physics or biology." -- Prové de l'editor Cover......Page 1 LONDON MATHEMATICAL SOCIETY LECTURE NOTE: SERIES......Page 3 Stochastic Stability of Differential Equations in Abstract Spaces......Page 5 Copyright......Page 6 Contents......Page 7 Preface......Page 9 1 Preliminaries......Page 13 2 Stability of Linear StochasticDifferential Equations......Page 58 3 Stability of NonlinearStochastic Differential Equations......Page 110 4 Stability of Stochastic FunctionalDifferential Equations......Page 190 5 Some Applications Related to StochasticStability......Page 238 Appendix A......Page 257 AppendixB......Page 259 AppendixC......Page 260 AppendixD......Page 262 References......Page 264 Index......Page 277 Preliminaries -- Stability Of Linear Stochastic Differential Equations -- Stability Of Non Linear Stochastic Differential Equations -- Stability Of Stochastic Functional Differential Equations -- Some Applications Related To Stochastic Stability. Kai Liu. Includes Bibliographical References (pages 252-264) And Index.