Numerical-analytical scheme for calculating the moment characteristics of the state vector of a stochastic differential-difference system

The paper is devoted to numerical-analytical scheme for calculating the moment functions of a random vector process that is a solution of the system of stochastic ordinary differential-difference equation (SODRE). The scheme consists of several subschemes and includes the adapted combination of the method of steps and expansion of the state space of the SODRE system, which transforms a non-Markov vector process into a chain of the Markov processes, a procedure for constructing calculation formulae for obtaining values of moment functions for state vectors with increasing dimension on a given grid, and an algorithm for recalculating the initial conditions step by step for the specified functions.