Moment equations for stochastic system special kind as instrument in apply problem

In paper considered the method of constructing moment equations for random solution of systems of nonlinear differential and difference equations, the right part of which depends on the stochastic process. Torque equations are constructed in the presence of jumps in solutions. For a system of differential equations with random coefficients, the case when the heterogeneous part of the system contains random processes such as white noise is considered. The ideas of A.M. Kolmogorov and V.I. Zubov on the analytical definition of random processes have been developed. In particular, non-Markov processes are investigated, which are determined by systems of linear differential equations with a delay in the argument. With the help of stochastic operators, fundamentally new results were obtained for non-Markov random processes, from which the main known results for Markov processes emerge. Methods and algorithms of analytical determination of finite-valued and infinite-digit random processes are proposed. The methods of studying the behaviours of the matrix of the second moments of some important classes of stochastic systems of equations are given because many optimization problems are reduced to the minimization of such a matrix. The substantiation of difference approximation for solving some types of differential equations used for the numerical solution of problems is carried out.