Joszef Lörinczi: Long and short time sample path properties of a class of Lévy-type processes

V četrtek, 29. marca 2018, ob 14:15 bo v predavalnici 3.06 Fakultete za matematiko in fiziko Univerze v Ljubljani na Jadranski ulici 21 v Ljubljani potekalo predavanje Joszefa Lörinczija, Loughborough University, UK, z naslovom Long and short time sample path properties of a class of Lévy-type processes.

Abstract: Lévy-type processes are currently a much researched class of jump processes, whose jump kernels are dependent on the current position in space. I will consider a subclass arising under perturbations of Lévy-processes, and look at their path properties on the short and long runs. To describe the short-time behaviour, I will present a result on the multifractal spectrum of local Hölder exponents of paths. In contrast, the long time behaviour depends on the tails of stationary densities, which allow to identify lower and upper envelopes for the time evolution profiles. I will also illustrate these results by some examples.