Ronnie Loeffen - Two-sided exit for the classical Markov branching process with immigration
|Starts:||15:00 13 Oct 2021|
|Ends:||16:00 13 Oct 2021|
|What is it:||Seminar|
|Organiser:||Department of Mathematics|
Ronnie Loeffen (University of Manchester) will speak in the Probability seminar.
We consider the classical Markov branching process introduced by Sevast'yanov (1957) which describes the size of a homogeneous population over time that allows for the arrival of immigrants into the population.
For this skip-free downward continuous time Markov chain we determine a semi-explicit expression for the probability that it exits a finite interval at the lower end point, which in particular generalises a known result for the case without immigration. Our approach is based on the framework for obtaining fluctuation identities for skip-free upward/downward discrete time Markov chains from Choi and Patie (2019).
This is joint work with P. Patie and J. Wang.
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