REMARKS ON NUMERICAL INTEGRATION OF STOCHASTIC DIFFUSION-TYPE EQUATIONS

摘要

A Langevin-type diffusion equation is studied by means of numerical integration .We show that the assumption of Gaussian white for the noise is occasionally invalid for stochastic diffusion equations such as the Edwards-Wilkinson equation in dimensions larger than two, because the derived results depend on discretized unit. Less singularly correlated noise is required to obtain reasonable results. The same situation can appear in a wide class of nonlinear stochastic partial differential equations.