Construction of integration by parts formulas

Abstract

In this chapter we construct integration by parts formulas in an abstract framework based on a finite-dimensional random vector $V = \left( {V_1 , \ldots ,V_J } \right);$ we follow [8]. Such formulas have been used in [8, 10] in order to study the regularity of solutions of jump-type stochastic equations, that is, including equations with discontinuous coefficients for which the Malliavin calculus developed by Bismut [17] and by Bichteler, Gravereaux, and Jacod [16] fails.