Forschungsseminar der Wahrscheinlichkeitstheorie: "First Exit Times for Lévy Driven Diffusions in Rd"

28.04.2015, 14:15-15:45  –  Am Neuen Palais, Haus 22 Raum 1.27
Forschungsseminar Wahrscheinlichkeitstheorie

André de Oliveira Gomes (Berlin)

It is our intention to describe the problem of the First Exit Time for dynamical systems perturbed in low intensity with jump noise. The problem of the First Exit Time can be viewed as the problem of understanding probabilistically (saying something about the expected value and the law) of the first time a certain stochastic process leaves a pre-established domain. It is known that a dynamical system never leaves the domain of attraction of a stable state after some time and it is remarkable that the excitation of the same dynamical system even in low intensity by a source of randomness ables the particle described by it to leave the same domain. With this kind of stochastic perturbation, it becomes interesting the problem of transition between the domains of attraction of the stable equilibria of the deterministic system. So the stable states become meta-stable and the stochastic perturbation determines their asymptotic dynamical properties. After presenting the state of the art in 1 d, we will address the problem in d-dimensions, in privilleged directions, and secondly we will solve the problem when the Lévy noise is an isotropic noise with exponentially lighted jumps, developing an analogue of the Freidlin-Wentzell Theory for this class of stochastic processes.