Event info

La Trobe-Kyushu Joint Seminar on Mathematics for Industry (6)

Date & Time : Aug. 25, 2015  13:00(Australian time) / 12:00(Japan time)
Venue: IMI Australia Branch in La Trobe University / Middle Meeting Room, IMI, Kyushu University
Title: Fractional Extensions of the Poisson process
Speaker: Professor Enzo Orsingher

Abstruct:

In this talk we consider several extensions of the Poisson process starting from the
• time-fractional Poisson process
We consider the equations governing the state probabilities and replace the time derivative with the so-called Djerbayshan-Caputo fractional derivative. We prove that the time-fractional Poisson process is a renewal process with Mittag-Leffler distributed intertimes;
• space-fractional Poisson process
We construct a Poisson process with independent increments and multiple jumps whose distribution satisfies the state-probabilities equation
∂pk =−λα(I−B)αpk, ∂t
where B is the shift operator;
• other generalizations of the Poisson processes are presented (which are weighted sums of the homogeneous Poisson process)
• the iterated Poisson process will be examined
• starting from
∂pk =−f(λ(I−B))pk ∂t
where f is a Bernstein function, we obtain generalized Poisson processes with multiple jumps and independent increments.