ABSTRACT
In this chapter, we shall present some selected topics in connection with stability properties of stochastic differential equations in infinite dimensions. The choice of the material reflects our own personal reference and the treatment here is somewhat sketchy. Some chosen material touches upon specific stochastic systems which could be regarded as a potential starting point for research in this area. Some other material reveals interesting and important relationships between the main topic, stability, of this book and topics from other branches of science or technology such as stochastic control. In particular, in Section 5.1 we shall begin with an exposition of stability for a class of stochastic parabolic equations with singular noise, e.g., distributed one. The problem of optimal feedback control and its relation with stablity of stochastic linear systems are studied in Section 5.2. Section 5.3 is wholly devoted to the investigation of feedback stabilization for a class of nonlinear stochastic models. In Sections 5.4 and 5.5, the stability results of the previous chapters are applied to some important models in chemical dynamics, fluid dynamics and mathematical population biology.
