An analysis of linear stochastic integro-differential systems with finite lumped delays

In the paper, a problem of derivation of ordinary differential equations for the first moment functions of the state vector for linear stochastic differential system with the special forms of delays, notably with finite lumped and variable lags, is considered. The technique, that combines the classic method of steps and the scheme of stochastic system state space's extension successively being developed by the author and transforms a vector non-Markov stochastic process into a Markov one, is used to derive a chain of stochastic differential equations without delays and then equations for required moment functions too.