Some notes on Malliavin calculus, surface integrals and integration by parts formulae in infinite dimensional spaces

Abstract:

We introduce a basic construction of the Malliavin calculus which unifies some different perspectives (e.g., Bogachev, Da Prato, Lunardi, Nualart). Then we introduce, for suitable functionals of the Brownian motion, the problem of  constructing a surface measure (i.e., the restriction of the reference measure on the infinite dimensional Wiener space) on the level sets defined by them.  Finally, we give some interpretation of such results in terms of other stochastic processes.