Stability of Infinite Dimensional Stochastic Differential Equations with Applications Monographs and Surveys in Pure and Applied Mathematics Series
Auteur : Liu Kai
Stochastic differential equations in infinite dimensional spaces are motivated by the theory and analysis of stochastic processes and by applications such as stochastic control, population biology, and turbulence, where the analysis and control of such systems involves investigating their stability. While the theory of such equations is well established, the study of their stability properties has grown rapidly only in the past 20 years, and most results have remained scattered in journals and conference proceedings.
This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics.
In recent years, this area of study has become the focus of increasing attention, and the relevant literature has expanded greatly. Stability of Infinite Dimensional Stochastic Differential Equations with Applications makes up-to-date material in this important field accessible even to newcomers and lays the foundation for future advances.
Date de parution : 09-2019
15.6x23.4 cm
Date de parution : 08-2005
15.6x23.4 cm
Thèmes de Stability of Infinite Dimensional Stochastic... :
Mots-clés :
Exponentially Stable; Null Solution; Mild Solutions; Stochastic Evolution Equations; Real Separable Hilbert Space; Asymptotic Stability; Strong Solution; Bounded Linear Operators; Invariant Measure; Lyapunov Functions; Global Strong Solution; Banach Space; Ultimately Bounded; Markov Process Xt; Stochastic Equations; Stochastic Navier Stokes Equations; Separable Banach Space; Stochastic Integrals; Unique Mild Solution; Lipschitz Continuous Function; Stochastic Parabolic Equations; Solution Xt; Nonnegative Continuous Function; Totally Bounded; Nonlinear Stochastic Systems