Journal of the
Korean Mathematical Society JKMS

In this paper, we consider a class of periodic It$\rm\hat{o}$ stochastic delay differential equations by using the properties of periodic Markov processes, and some sufficient conditions for the existence of periodic solution of the delay equations are given. These existence theorems improve the results obtained by It$\rm\hat{o}$ et al.~\cite{Ito2}, Bainov et al.\cite{Bainov} and Xu et al.~\cite{Xu1}. As applications, we study the existence of periodic solution of periodic stochastic logistic equation and periodic stochastic neural networks with infinite delays, respectively. The theorem for the existence of periodic solution of periodic stochastic logistic equation improve the result obtained by Jiang et al.~\cite{Jiang1}.

Keywords: stochastic differential equations, periodic solution, infinite delay, logistic equation, neural networks

MSC numbers: 34A37, 34D23