6th World Congress on Physics
Université de Franche Comté, France
Title: Some relations between bounded below elliptic operators and stochastic analysis
Biography: Rémi Léandre
Some relations between bounded below elliptic
operators and stochastic analysis
We adapt Bismuth’s way of the Malliavin calculus to a class of elliptic rightinvariant pseudo-diff erential operators on a Lie group bounded below on a Lie group. Unlike the standard Malliavin calculus for Poisson processes, there is no limitation on the size of big jumps (small values of the extra-variables in the symbol of the operator). In the second step, we establish the link of big order non-Markovian generator of Poisson type and the theory of bounded below operators by using Garding inequality.