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

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.

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Acknowledgment

This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University.