Spectral Representations of Iterated Stochastic Integrals and Their Application for Modeling Nonlinear Stochastic Dynamics

Spectral representations of iterated Itô and Stratonovich stochastic integrals arbitrary multiplicity, including from Taylor–Itô Taylor–Stratonovich expansions, are obtained by the spectral method. They required for implementation numerical methods solving differential equations with high orders mean-square strong convergence. The purpose such is modeling nonlinear dynamics in many fields. This paper contains necessary theoretical results, as well results experiments.