Stability theory of stochastic differential stems

tability in the Lyapunov sense for deterministic systems has been well studied since the beginning of this century. Since the middle of this century, Lyapunov method has been used to study stability and controllability of stochastic differential systems both in finite and infinite dimensional spaces. The sufficient and necessary conditions for exponential stability in p-th mean of Ito type nonlinear stochastic differential equations was obtained. At the same time, practically stability of deterministic differential systems was also studied. Since the late 80's, practical stability in mean of stochastic differential systems has been studied. The theory of stochastic integral of processes which are not necessarily adapted has been developed by many authors. The stochastic Volterra equations have been discussed recently, which arise in applications particularly in finance theory.;The present thesis studies the stability several directions. Firstly, weak exponential stability of nonlinear Ito type stochastic differential systems and related controlled problems are discussed, the conditions for this kind of stability are obtained. Secondly, exponential stability of...