Stochastic integro-differential equations with nonlocal conditions and infinite delay.

Abstract

Many stochastic systems arising in nature exhibit hereditary properties; that is ; state depends on the past time history. The time history dependence of state renders the equation of motion of stochastic systems in the form of stochastic integro-differential equations. The research reported in this thesis deals with the problem of stochastic integro-differential systems with delay. More precisely, existence of solution for stochastic integro-dffeerential equations in Hilbert space with infinite delay . We first prove the existence of mild solutions for a class of fractional neutral stochastic integro-differential equations with infinite delay. Secondly, we explore the existence results with nonlocal conditions. Our approach and technique is mainly based on fixed point theorem and C_{0} semigroups theory.