  Let the process Y(t) be a Skorohod integral process with respect to Brownian
motion. We use a recent result by Tudor (2004), to prove that Y(t) can be
represented as the limit of linear combinations of processes that are products
of forward and backward Brownian martingales. Such a result is a further step
towards the connection between the theory of continuous-time (semi)martingales,
and that of anticipating stochastic integration. We establish an explicit link
between our results and the classic characterization, due to Duc and Nualart
(1990), of the chaotic decomposition of Skorohod integral processes. We also
explore the case of Skorohod integral processes that are time-reversed Brownian
martingales, and provide an "anticipating" counterpart to the classic Optional
Sampling Theorem for It\^{o} stochastic integrals.
