Forward integration, convergence and non-adapted pointwise multipliers

Abstract

In this paper we study the forward integral of operator-valued processes with respect to a cylindrical Brownian motion. In particular, we provide conditions under which the approximating sequence of processes of the forward integral, converges to the stochastic integral process with respect to Sobolev norms of smoothness α < 1/2. This result will be used to derive a new integration by parts formula for the forward integral.