Forschungsseminar der Wahrscheinlichkeitstheorie: "Large Deviations Theory for Lévy Processes and Applications"

14.04.2015, 14:15-15:45  –  Am Neuen Palais, Haus 22 Raum 1.27
Forschungsseminar Wahrscheinlichkeitstheorie

André de Oliveira Gomes (Berlin)

We review the Weak Convergence Approach to Large Deviations Theory, developed by Budhiraja, Dupuis and Ellis in 2009. We construct the Large Deviations Principle for certain collections of Poisson Random Measures, using variational representations and properties of the relative entropy, with very weak assumptions on the Lévy measure of the underlying processes. As a first application we derive a Large Deviations Principle for a Compound Poisson Process. As a second application, motivated by the problem of the vanishing viscosity for a fluid with a nonlocal source of diffusion, we use this theory to study the asymptotic behavior of a Forward-Backward system of SDE with Jumps, that can be seen as the probabilistic counterpart of this analytical problem.