Some moment estimates for new semi-implicit split-step methods

Abstract

In this work, we introduce alternative numerical procedures based on a combination of split-step and partially implicit methods to solve a class of nonlinear stochastic differential equation that arise from certain physical and financial applications. Considering certain monotonicity and polynomial growth conditions, we focus on the moment estimates of both the actual and the numerical solutions of a generalized version of stochastic Ginzburg-Landau equations.