An analysis of linear stochastic systems with constant delays and discrete and continuous fluctuations

In the paper, we consider a problem of calculation of the first moment functions for the state vector of linear stochastic difference-differential system excited by random Wiener and Poisson processes. The technique combining the classic method of steps and the scheme of phase space extension is used to derive a chain of integro-differential Kolmogorov - Feller equations satisfied by joint probability density functions and then to obtain ordinary differential equations for required moment functions without delays.