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DCDS

In this paper, an effective existence theorem for periodic Markov
process is first established. Using the theorem, we consider a class
of periodic $It\hat{o}$ stochastic functional
differential equations,
and some sufficient conditions for the existence of periodic
solution of the equations are given. To overcome the difficulties
created by the special features possessed by the periodic stochastic
differential equations with delays, as one will see, several lemmas
are introduced. These existence theorems are rather general and
therefore have great power in applications. Especially, our results
are natural generalization of some classical periodic theorems on
the model without stochastic perturbation. An example is worked out
to demonstrate the advantages of our results.

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