Existence and uniqueness of the solutions of delay stochastic integral equations

Abstract

In I 1 1 we studied the existence and uniqueness of solutions to the following typical stochastic integral equation with respect to semimartingales This paper is devoted to the existence and uniqueness of solutions to the following delay stochastic integral equation where Xd=(Xd(t)) is said to be the delay process of X defined as follows: in which is a continuous function satisfies some conditions. We should point out that our results can be generalized to the more general equation without any difficulty, where X and Xd are n-dimensional stochastic processes and semimartingales

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