Abstract for the talk on 20.06.2017 (15:15 h)Oberseminar ANALYSIS - PROBABILITY
Anthony Réveillac (INSA de Toulouse)
Stochastic regularization effects of semi-martingales on random functions
Since the late 70s it is well-known that the addition of a random force in an ill-posed ODE may bring back the system well-posed. This kind of phenomenon is known as ”stochastic regularization effect” or ”regularization by noise”. A breakthrough in this domain is contained in the paradigm known under the name of ”The Itô-Tanaka trick” which links the time average of a non-smooth map f along the solution of an SDE with the solution of a Fokker-Planck PDE. However, this approach is restricted to deterministic mappings f. The aim of this talk is to go beyond this limitation. More precisely, we propose an extended version of the Itô-Tanaka trick to random mappings f. This talk is based on a joint work with Romain Duboscq.