Section: New Results

Regularity of probability laws using an interpolation method

Participant : Vlad Bally.

The distance between two density functions and convergence in total variation. In collaboration with Lucia Caramellino we obtained estimates of the distance between the densities of the law of two random variables using an abstract variant of Malliavin calculus. We used these estimates in order to study the convergence in total variation of a sequence of random variables. This has been done in [47] . We are now working on more specific examples concerning the Central Limit Theorem. In the last years the convergence in entropy distance and in total variation distance for several variants of the CLT has been considered in papers of S. Bobkov, F. Gotze, G. Peccati, Y. Nourdin, D. Nualart and G. Polly. So this seems to be a very active research area. Moreover, in an working paper in collaboration with my Phd student R. Clement, we use the same methods in order to study the total variation distance between two Markov semigroups and in particular for approximation schemes. A special interest is devoted to higher order schemes - as for example the Victoire Nyomia scheme.