The asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching and with polynomial growth

This paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with Markovian switching (SDSwMSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, we propose some conditions under which such SDSwMSs are asymptotically stable and exponentially stable. Nontrivial examples are provided to illustrate our results.