Zusammenfassung für den Vortrag am 10.03.2016 (15:15 Uhr)

Oberseminar ANALYSIS - PROBABILITY

Paul Gassiat (Université Paris Dauphine)
Malliavin Calculus for the nonlinear Parabolic Anderson Model

Many nonlinear stochastic PDES arising in statistical mechanics are ill-posed in the sense that one cannot give a canonical meaning to the nonlinearity. Nevertheless, Martin Hairers theory of regularity structures provides us with a good notion of solution for a large class of such equations (KPZ equation,stochastic quantization,...). One of the simplest equations to which this theory can (and should) be applied is the generalized 2D Parabolic Anderson Model : <center class="math-display"> <img src="/fileadmin/lecture_img/tex_18395c0x.png" alt="(∂t − Δ )u = f(u)ξ,u (0) = u0, " class="math-display"></center>

where ξ is a spatial white noise on the torus