Stability of Infinite Dimensional Stochastic Differential Equations with Applications

Focusing on the stability of stochastic differential equations in infinite dimensional spaces, particularly Hilbert spaces, this book systematically presents both linear and nonlinear stability theories. It reviews essential concepts and delves into stochastic functional differential equations. The final chapter covers advanced applications, including stochastic optimal control, feedback stabilization, and dynamics related to Navier-Stokes equations and population dynamics. This comprehensive treatment not only makes current material accessible but also establishes a foundation for future research developments.