Stability of the Stochastic Differential Equations

Abstract

Stability of stochastic differential equations (SDEs) has become a very popular theme of recent research in mathematics and its applications. The method of Lyapunov functions for the analysis of qualitative behavior of SDEs provide some very powerful instruments in the study of stability properties for concrete stochastic dynamical systems, conditions of existence the stationary solutions of SDEs and related problems. The study of exponential stability of the moments makes natural the consideration of certain properties of the moment Lyapunov exponents. Another important characteristic for stability (or instability) of the stochastic systems is the stability index.