Nonlocal Cauchy problem for some stochastic integro-differential equations in Hilbert spaces

In this paper, we study the existence results of mild solutions for a class of stochastic integro-differential equations with nonlocal conditions and stochastic impulsive integro-differential equations with nonlocal conditions in Hilbert spaces. Sufficient conditions for the existence of mild solutions are derived by means of Leray-Schauder nonlinear alternative. An example is provided to illustrate the theory.