A Wong–Zakai type approximation for two-parameter processes1

Abstract

We present an extension of the Wong–Zakai approximation theorem for a stochastic differential equation on the plane driven by a two-parameter Wiener process. For an approximation of the two-parameter Wiener process, we use a two-parameter version of the one-parameter piecewise linear approximation. By our approximation to the two-parameter Wiener process we show that the solution of an ordinary differential equation converges, in the uniform L 2-sense, to that of a stochastic differential equation obtained by using Stratonovich integral. *This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.