Generalized multiple stochastic integrals and the representation of wiener functionals
- 1 March 1988
- journal article
- Published by Taylor & Francis in Stochastics
- Vol. 23 (3) , 311-330
- https://doi.org/10.1080/17442508808833496
Abstract
In this paper we study a generalized multiple stochastic integral for non-adapted integrands following Skorohod's approach. The main properties of this integral are derived. In particular, we prove a Fubini type result and discuss the relation of this multiple integral to the Malliavin calculus. It turns out that this integral includes other kinds of multiple stochastic integrals like those of Hajek and Wong. Finally, we apply these results to the representation of functionals of the multiparameter Wiener process, obtaining explicit formulas for the kernels of the representation in terms of conditional expectations of Malliavin derivativesKeywords
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