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.
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