| In this paper,the existence,uniqueness and stability of solutions of stochastic delay differential equations with Markovian switching driven by L évy noise are studied.The existence and uniqueness of the solution of the equation are proved by Picard iterative method.Using Lyapunov-Krasovskii function and stochastic analysis theory,the p(p ≥ 2)-moment exponential stability,almost surely exponential stability and stochastic input state stability of stochastic delay differential equations with Markov switching driven by L évy noise are studied.Specifically,the main contents of this paper are as follows:The first chapter introduces the research background,significance,main work,innovation and preparatory knowledge of this paper.In Chapter 2 when the drift term and diffusion term satisfy the global lipschitz condition,the existence and uniqueness of solutions of stochastic delay differential equations with Markovian switching driven by L évy noise are proved by using Picard iterative method and stochastic analysis theory.Using the generalized integral inequality,Lyapunov-Krasovskii function and stochastic analysis theory,the p(p ≥ 2)-moment exponential stability and almost surely exponential stability of the equation are studied.In Chapter 3 under the condition that the drift term and diffusion term satisfy the global Lipschitz condition,the p(p ≥ 2)-moment input state exponential stability and random input state exponential stability of the solutions of stochastic delay differential systems with Markovian switching driven by L évy noise are studied by using the generalized delay integral inequality,Lyapunov-Krasovskii function and stochastic analysis theory.The fourth chapter is the summary and prospect. |
