A Fubini Theorem for Generalized Stratonovich Integrals

Abstract

The purpose of this paper is to analyze under which conditions the multiple generalized (that means, non necessarily adapted) Stratonovich integral with respect to the Brownian sheet can be iterated. The motivation of this problem comes from a previous work by the authors. Indeed, in [2] an iteration of a double Stratonovich integral with respect to a non adapted “semimartingale” in the plane is needed in order to prove a Green formula. In comparison with that article the situation considered here is more simple, since our integrator is the Brownian sheet, but also more general, because we are considering multiple integrals of any order k ≥ 2. The basic ingredients which are needed are the Hu-Meyer formula established in [1], the Fubini’s theorem for the multiple Skorohod integral (see [3]) and some results on the iteration of traces.

Partially supported by the DGICYT grant no. PB 90-0452