An approximate formula for calculating the expectations of functionals from random processes based on using the Wiener chaos expansion

In this work, we propose a new method for calculating the mathematical expectation of nonlinear functionals from random processes. The method is based on using Wiener chaos expansion and approximate formulas, exact for functional polynomials of given degree. Examples illustrating approximation accuracy are considered.

Stochastic elastic equation driven by multiplicative multi-parameter fractional noise

In this paper, we consider the stochastic elastic equation driven by multiplicative multiparameter fractional noise. By using the Wiener chaos expansion and undetermined coefficient methods, we obtain the existence and uniqueness of the solution in a distribution space. The asymptotic behavior and the Hölder index of the solution are also estimated.