On Some Methods for Study of Stochastic Hereditary Systems

Abstract

Different types of stochastic retarded systems could be considered on the base of our schemes of phase space extension. This scheme is applicable for investigation of linear and nonlinear differential difference equations with single and multiple constant delays, differential equations with variable delays, neutral delay differential equations etc. In addition, a combination of the scheme and the Monte Carlo method can be exploited for study sophisticated objects. The main topic of research in this paper is the problem of computation of the first moment functions for the phase vectors defining states for linear stochastic systems of differential equations with the special form of variable delays, notably with piecewise constant delays, and integro-differential equations.