Integration by parts formulae for Wiener measures restricted to subsets in Rd

We study an integration by parts formula for a pinned Wiener measure restricted to a space of paths staying within a subset in Rd. The result presented here generalizes the formula in [L. Zambotti, Integration by parts formulae on convex sets of paths and applications to SPDEs with reflection, Probab. Theory Relat. Fields 123 (2002) 579–600] for the case of a half-line in R.