Skorohod stochastic integration with respect to non-adapted processes on wiener space

Abstract

We define a Skorohod type anticipative stochastic integral that extends the Itô integral not only with respect to the Wiener process, but also with respect to a wide class of stochastic processes satisfying certain homogeneity and smoothness conditions, without requirements relative to filtrations such as adaptedness. Using this integral, a change of variable formula that extends the classical and Skorohod ltô formulas is

obtained

Keywords:

• Itô calculus
• Malliavin calculus
• Skorohod integral
• Mathematics Subject Classification (1991): 60H05, 60H07