About a symbolic and numeric scheme for a calculation of the first moment functions for the state vectors of linear stochastic integro-differential systems

In this paper we consider an approximate scheme for an analysis of linear dynamic system described by stochastic integro-differential equations. The scheme is based on a local approximation of kernels of these equations allowing to transform the original equations to a system of linear stochastic differential equations on the basis of a state space expansion and, consequently, to construct a chain of closed ordinary differential equations to calculate the first moment functions of the system state vector.