A Wong-Zakai type approximation for multiple Wiener-Stratonovich integrals

Abstract

We present an extension of the Wong-Zakai type approximation theorem for a multiple stochastic integral. Using a piecewise linear approximation w((n)) of a Wiener process w, we prove that the multiple integral process {integral(0)(t)...integral(0)(t) f(t(1),..., t(m))dw(t1)(n...)dw(tm)(n), t is an element of [0, T]}, where f is a given symmetric function in the space C([0, T](m)), converge to the multiple Stratonovich integral of f in the uniform L-2-sense.