[PDE & Applications seminar] Zivorad Tomovski: Fractional Poisson process and Applications

20 april 2023 16:00 t/m 17:00 - Locatie: Snijderszaal LB 01.010 EEMCS | Zet in mijn agenda

The name fractional Poisson process is due to Laskin 2003 who
derived the
one point counting distribution. The renewal process of Mittag Leffler
type was discussed by Gorenflo, Mainardi and Scalas in two papers
published in 2004 one of them specifically devoted to the process and
published
on the Vietnam Journal of Mathematics. Hilfer and Anton 1995 were the first
to recognize the relation between the Mittag Leffler function and the time
fractional diffusion equation. The use of the Mittag Leffler function in
this
framework can be traced back to works of Gnedenko and Kovalenko 1968 on
thinning and Balakrishnan 1985 on anomalous diffusion. We will discuss
fractional
Poisson process by considering Hilfer-Prabhakar derivative in
difference-differential equations governing the dynamics of generalized
renewal stochastic processes.