On Numerical Modeling of the Multidimentional Dynamic Systems under Random Perturbations with the 2.5 Order of Strong Convergence

Abstract

Numerical modeling methods with a strong convergence of order 2.5 are developed for the multidimensional dynamic systems under random perturbations described by Itô stochastic differential equations. Special attention is paid to the numerical modeling methods of the multiple Itô stochastic integrals of multiplicities 1–5 in terms of the mean-square convergence criterion, which are required to implement the former methods.