Existence theorems for non-linear random integral equations with time lags

Abstract

Two basic forms of non-linear random integral equations are studied and where being the underlying set of a complete probability measure space (fi, A, P). The random process x(t; ω) is the unknown random function is the stochastic free term; the stochastic kernels are of convolution type, of linear and non-linear form, respectively, defined for and the processes are scalar functions defined for tsR+ and x£R.The object of this paper is to develop sufficient conditions for the existence of a, random solution, a second-order stochastic process, to the above equations. We utilize the methods of successive stochastic approximation and Banach's fixed point theorem to fulfil the objective.