Perpetual integral functionals of Brownian motion

Date/heure
4 mai 2017
10:45 - 11:45

Oratrice ou orateur
José Alfredo Là³pez Mimbela

Catégorie d'évènement
Séminaire Probabilités et Statistique


Résumé

We consider semi-linear PDEs perturbed by a multiplicative noise
of the form

$
du(t,x)=[Au(t,x)+G(u(t,x))]dt+ku(t,x)dW(t),
$

where $ A$ is the Laplacian, $ G$ is a positive, increasing convex function, $ k
$ is constant and $ {W(t)}$ is a one-dimensional Brownian motion.
Nontrivial positive solutions of these equations can exist globally in time,
or they can exhibit blow up in finite time. In this talk we will focus on
the later regime and obtain bounds for the blow up times, which are given in
terms of integral functionals of $ {W(t)}$.