Characterization of infinite divisibility by duality formulas. Application to Lévy processes and random measures (Q1947603)

This paper is devoted to various characterizations of probability measures via Malliavin derivatives and finite difference operators, in particular for infinitely divisible distributions and processes with independent increments. The classical Brownian and Poisson examples are considered first, followed by a natural extension of integration by parts characterizations to infinitely divisible random vectors, with application to processes with independent increments and infinitely divisible random measures. The integration by parts formulas are obtained by direct computations based on the Lévy-Khintchine formula instead of relying on multiple stochastic integral expansions as done by other authors. Links with the finite-dimensional Stein and Chen-Stein equations are pointed out.