Asymptotic Exponential Stability for Diffusion Processes Driven by Stochastic Differential Equations in Duals of Nuclear Spaces

Abstract

The main objective of this paper is to investigate the asymptotic stability for diffusion processes driven by a class of Itô stochastic differential equations in duals of nuclear spaces. A coercivity condition imposed on this sort of equation plays the role of an exponential stability criterion. An example is studied to illustrate our theory.