Stochastic Stability Of Stochastic Differential Systems With Renewal Process

Since the theory stochastic differential equations have been established, it has been widely applied in natural science, engineering technology,etc. But, these equations as a kind of important mathematica model, during the practical application, random dynamical systems are affected by some uncertain factors, such as the changes of environment, etc, leading to instability of the systems. Therefore we can use proper switching to get a certain degree of stability.In this paper, we investigate the stability of stochastic differential systems with Re-newal process switching, this Renewal process is defined on a filtered probability space. First of all, we can transform this kind of stochastic differential systems to Markov pro-cess, and define its generators under suitable condition. Moreover, we give some sufficient conditions for their exponential stability with Renewal process switching.