Stochastic periodic solutions of stochastic differential equations driven by Lévy process

In this paper, a class of periodic stochastic differential equations driven by Lévy processes (SDEsLP) is studied. Firstly, we give the existence–uniqueness theorem for a large class of SDEsLP. Then, using the properties of the periodic Markov processes, sufficient conditions for the existence and uniqueness of periodic solution to the periodic SDEsLP are given. Finally, an example is introduced to illustrate the results developed.