Existence and uniqueness theorems for periodic Markov process and applications to stochastic functional differential equations

This work is devoted to an M-valued Markov process with a periodic transition probability function, where M is a Polish space. Sufficient conditions for the existence and uniqueness of the periodic Markov process are given. These existence theorems are rather general and the corresponding results in [1], [11], [15], [23] are improved and generalized. The uniqueness theorems for the periodic Markov process are original. As applications, we study the existence, uniqueness and global attractivity of periodic solution for the periodic stochastic n-species Lotka-Voltrra competitive model with bounded delays and the periodic stochastic neural networks with infinite delay, respectively. Numerical simulations are presented to illustrate the main results.