Abstract:

This paper is concerned with the existence and uniqueness of solution for a class of stochastic functional equation: X = (X), where
: B ! B and B is a Banach spaceconsisted of all left-continuous, (Ft)-adapted processes. Also, the main result is applied tosome S.D.E (or S.I.E.). And the authors adopted some of the results in current research in the models of stochastic control recently. This paper proves the existence and uniquence and uniqueness of solution for stochastic functional equation. A series of corollaries are deduced from the special examples of the theorems in this paper.

Key words: Stochastic functional equation, stochastic differential (integral) equation,principle of contraction mapping