Projecting Multiple Stochastic Integral unto the Wiener Functional Space Using Iterated Integrals

Any square- integrable functional of the Wiener process has a canonical representation in terms of the integrals. The key of these representation is to define multiple stochastic integral of the form  where φ is (in general) a random integrand-adapted in a suitable sense. In this paper, we construct projections with respect to stochastic integral unto the Wiener functional space and establish formulae for the transformation of multiple stochastic integrals under two operations; (a) projection formula for the projection of a multiple stochastic integrals onto and (b) an iterated formula.