On forward stochastic integrals over the loop space

Let M be a complete and compact Riemannian manifold, m(0) a fixed point of M, and gamma the pinned Brownian motion based at m(0). In this note, we define a forward stochastic integral with respect to gamma. We show that it is an extension of the usual It stochastic integral for adapted processes in L-2 (T-m 0(M)), give a substitution formula for a large class of processes, and then show a change of variable formula in this context.