Abstract:
Exponential functionals of Lévy processes have been widely studied over the past years and have multiple applications, among which the study of diffusions in random environment, the study of self-similar Markov processes or mathematical finance. We are interested in functionals of spectrally one-sided Lévy processes conditioned to stay positive and establish some of their properties: finiteness, distribution tails, self-decomposability, smoothness of the density. We then apply these properties to the study of the asymptotic behavior of the local time of a diffusion in a spectrally negative Lévy environment.
Biography:
Grégoire Véchambre is a Postdoctoral Research Fellow at NYU Shanghai. He holds a Ph.D. from Orléans University, received in November 2016, and prepared under the supervision of Dr. Pierre Andreoletti. His research interests include self-interacting processes, processes in random environments, Lévy processes and related processes, and exponential functionals of Lévy processes.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai