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
∂p_k/∂t =−λ^α(I−B)^αp_k,
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
∂p_k/∂t =−f(λ(I−B))p_k
where f is a Bernstein function, we obtain generalized Poisson processes with multiple jumps and independent increments.
Book your nearest ACE facility (check which universities currently have an ACE facility: https://rhed.amsi.org.au/ace/)
How to participate in this seminar:
1. Book your nearest ACE facility;
2. Notify the ACE contact person at the host institution (Darren Condon) to notify you will be participating.
No access to an ACE facility? Contact Maaike Wienk to arrange a temporary Visimeet licence for remote access (limited number of licences available – first come first serve)