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Seminari di Probabilità e Finanza Matematica: SDEs with distributional drift and Polymer measure; (Local) CLT for symmetric Diffusions in a degenerate Random Environment

Giovedì 12 Febbraio 2015, ore 14:30 - Aula 2BC30 - Giuseppe Cannizzaro e Alberto Chiarini

ARGOMENTI: Seminari

Seminari di Probabilità e Finanza Matematica

Giovedì 12 Febbraio 2015 in aula 2BC30 si terranno i seguenti seminari:

Ore 14:30 - 15:30
Giuseppe Cannizzaro (Technical University of Berlin) "SDEs with distributional drift and Polymer measure".

Abstract
We study existence and uniqueness of solution for stochastic differential equations with distributional drift by giving a meaning to the Strook-Varadhan martingale problem associated to such equations. The approach we exploit is the one of paracontrolled distributions recently introduced by Gubinelli, Imkeller and Perkowski in their by now celebrated paper "paracontrolled distributions and singular PDEs." As a result, we make sense of the two and three dimensional polymer measure and show some of its properties.

Ore 15:30 - 16:30
Alberto Chiarini (Technical University of Berlin) "(Local) CLT for symmetric Diffusions in a degenerate Random Environment".

Abstract
We study a symmetric diffusion $X$ on $\mathbb{R}^d$ in divergence form in a stationary and ergodic environment, with measurable unbounded and degenerate coefficients. The diffusion is formally associated with $L^\omega u = \nabla\cdot(a^\omega\nabla u)$. We prove for $X$ a quenched (local) central limit theorem, under some moment conditions on the environment; the key tools are the sublinearity of the corrector and a parabolic Harnack's inequality both obtained using the celebrated Moser's iteration technique.