Approximate Formulas for Mathematical Expectations of Functionals of Random Processes Defined by Ito-Levy Multiple Integral Expansion

An approximate formula is constructed for calculating mathematical expectations of nonlinear functionals of random processes defined by chaotic expansions in terms of multiple Ito-Levy integrals. We consider the possibility of applying the formula to the calculation of mathematical expectation of functionals corresponding to the solution of one kind of Skorokhod equations on a Wiener process. Test examples of computations using the constructed formula for particular cases of Levy process are presented. The elaborated method gives a new useful tool for numerical integration with a required accuracy of stochastic differential equations which are reduced to the Skorokhod class of equations.