Statistica Sinica 7(1997), 907-922

TWO RESULTS ON MULTIPLE STRATONOVICH INTEGRALS

A. Budhiraja and G. Kallianpur

University of North Carolina, Chapel Hill

Abstract: Formulae connecting the multiple Stratonovich integrals with single Ogawa and Stratonovich integrals are derived. Multiple Riemann-Stieltjes integrals with respect to certain smooth approximations of the Wiener process are considered and it is shown that these integrals converge to multiple Stratonovich integrals as the approximation converges to the Wiener process.

Key words and phrases: Multiple Stratonovich integrals, multiple Wiener integrals, Wong-Zakai approximations.