Section: New Results

Malliavin calculus and applications

Lower bounds for the density of functionals on the Wiener space

In collaboration with: B. Fernandez and A. Meda from the University of Mexico, V. Bally gave a lower bound for general Itô processes to remain in a tube around a given curve. This is done under some ellipticity assumption in [21] . Now, with L. Caramellino (University Tor Vergata, Rome) he investigates the case of a diffusion processes which satisfies the Hörmander condition.

Malliavin Calculus for Poisson Point Processes and applications

V. Bally and E. Clément (Université Paris-Est Marne la Vallée) study the density of the law of the solution of a stochastic equation with jumps, which has discontinuous coefficients [18] , [19] . Moreover, with N. Fournier (university of Creteil), V. Bally obtained results on the smoothness of the law of a bidimensional Bolzman equation [22] .

Riesz transform and regularity of the law of a random variable

The idea of using the Riesz transform in order to study the regularity of the law of a random variable appears in former works of P. Malliavin and A. Thalmaier. In collaboration with L. Caramellino (University Tor Vergata, Rome) we gave regularity results using this tool [17] .