V. Shcherbakov - Long term behavior of linear competition processes.

schedule le mardi 21 janvier 2020 de 14h00 à 15h00

Organisé par : LPSM

Intervenant : Vadim Shcherbakov (Royal Holloway University of London)
Lieu : Jussieu, tours 16-26, 2ème étage, salle 209.

Sujet : V. Shcherbakov - Long term behavior of linear competition processes.

Résumé :

Long term behavior of linear competition processes.



Abstract:


Competition process is a multivariate analogue of the classical birth-and-death process originally motivated by modelling competition between populations. Competition process can be interpreted as a system of interacting birth-and-death processes, the components of which evolve subject to a competitive interaction. In my talk, I will discuss the long term behaviour of a version of such a process, where a component increases with a linear rate and decreases with the rate given by a linear function of other components. If a component becomes zero, it stays zero forever (we say that the component becomes extinct). We prove that, with probability one, eventually only a random subset of non-interacting components survives. The dynamics of the model has a striking resemblance with that of multi-type branching processes, which allows us to adapt ideas from the well-known Athreya's method for studying the long-term behaviour of the branching processes.


The talk is based on joint work with S. Volkov (Lund University).