Stability And Boundedness Of Nonlinear Hybrid Stochastic Differential Delay Equations

This dissertation mainly investigates the long-time dynamical behaviors of nonlinear hy-brid stochastic differential delay equations.The key contributions of this paper are as follows:(i)For hybrid systems with finite and irreversible state spaces,we utilize Perron-Frobenius theorem to construct the Lyapunov functions depending on discrete states and yield moment boundedness,moment exponential stability and almost sure stability.And for the case of finite and reversible Markov chain,we derive asymptotic mean square boundedness,mean square stability and almost sure stability by using the principal eigen-value approach.(ii)For hybrid systems with infinite countable state spaces,we obtain asymptotic mean square boundedness,mean square stability and almost sure stability by the finite partition method and the M-Matrix theory.Several nonlinear examples are also given to illustrate our results.