Anticipatory Itô's formula and Hitsuda-Skorokhod integral (Q2726268)

In the seventies \textit{M. Hitsuda} [in: Proc. 2nd Japan-USSR Symp. Probab. Theory 2, 11-114 (1972)] and \textit{A. V. Skorokhod} [Theory Probab. Appl. 20, 219-233 (1975); translation from Teor. Veroyatn. Primen. 20, 223-238 (1975; Zbl 0333.60060)] defined independently the integral over Brownian motion with anticipating function as integrand. It is known now as the Hitsuda-Skorokhod (HS)-integral. For nonanticipating functions the (HS)-integral coincides with the Itô integral. Therefore, the (HS)-integral is an extension of the Itô integral for integrands that may be anticipating. White noise calculus provides a very natural tool to study stochastic integrals. And the (HS)-integral can be expressed in terms of white noise calculus. Let \(\mu\) be the standard Gaussian measure on \(S'(R).\) The Hitsuda-Skorokhod integral is expressed as a white noise integral which defines a random variable in \(L^{2}(\mu),\) or more generally, in \(L^{p}(\mu)\) for some \(p> 1.\) An anticipatory Itô formula is proved for the stochastic process \(\theta(X(t),X(c))\) with \(X(t)\) being a Wiener integral. The formula is related to the (HS)-integral.NEWLINENEWLINEFor the entire collection see [Zbl 0956.00022].