Henri Elad Altman - Formules de Bismut Elworthy Li pour les processus de Bessel
Channel: Institut des Hautes Études Scientifiques (IHÉS)
Date: 2017-05-18

Bessel processes are a one-parameter family of nonnegative diffusion processes with a singular drift. When the parameter (called dimension) is smaller than one, the drift is non-dissipative, and deriving regularity properties for the transition semigroup in such a regime is a very difficult problem in general.
In my talk I will show that, nevertheless, the transition semigroups of Bessel processes of dimension between 0 and 1 satisfy a Bismut-Elworthy-Li formula, with the particularity that the martingale term is only in L^{p} for some p more than 1, rather than L^{2} as in the dissipative case. As a consequence some interesting strong Feller bounds can be obtained. 

http://www.lesprobabilitesdedemain.fr/
Organisateurs : Linxiao Chen, Sophie Laruelle, Pascal Maillard, Bastien Mallein, Damien Simon et la Fondation Sciences Mathématiques de Paris
Soutiens : LabEx Mathématiques Hadamard et École Doctorale Mathématiques Hadamard.