Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Stability of Infinite Dimensional Stochastic Differential Equations with Applications presents up-to-date, complex material in an accessible way. Focusing mainly on Hilbert spaces, this book features an in-depth discussion of infinite dimensions, including the notion of L2-stability in mean. It investigates stability for the essential classes of linear stochastic evolution equations. Additional material explores topics related to the stability of nonlinear systems and equations. With various stability models and applications for both finite and infinite dimensions, this text is an ideal reference for graduate students, researchers, engineers, and scientists interested in this area. According to the EMS Newsletter, "This book can be recommended to everybody interested in an advanced theory of stochastic differential and, in particular, in the stability problem."

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.

Stochastic Differential Equations in Infinite Dimensions. Stability of Linear Stochastic Differential Equations. Stability of Non Linear Stochastic Differential Equations. Stability of Stochastic Functional Differential Equations. Some Related Topics of Stability and Applications.

Liu, Kai