Controllability of semilinear stochastic control system with finite delay.

The objective of this paper is to present some sufficient conditions for approximate and exact controllability of semilinear stochastic control system with finite delay. Sufficient conditions for approximate controllability are obtained by separating the given semilinear system into two systems namely a semilinear deterministic system and a linear stochastic system using Schauder fixed point theorem. For obtaining the sufficient conditions for exact controllability of assumed system, Banach fixed point theorem is applied. Instead of a C0-semigroup associated with the mild solution of the system we use the so-called fundamental solution. At the end, examples are given to illustrate the theory. [ABSTRACT FROM AUTHOR]