- Date: 3 Sep. (Thu.)
- Place: On the Web
- Time: 16:30-18:00
- Speaker: Linglong Yuan (University of Liverpool)
- Title: Limit theorems for continuous-state branching processes with immigration
- Abstract:
The continuous-state branching processes with immigration (CBI) arises in the literature of stochastic processes with a biological background.
Kawazu and Watanabe (1971) firstly introduced CBI and proved that it is the limit of a sequence of Galton-Waton discrete branching processes with immigration.
Since then CBI has received a lot of attention. It is connected to stochastic differential equations, Levy processes, population modelling etc. In mathematical finance, a special kind of CBI is called Cox–Ingersoll–Ross model which is well known to describe the evolution of interest rates. In this talk, we will briefly introduce CBI and focus on the long term behavior which turn out to have two different regimes. In the first one, an almost sure convergence is proved adapting the Grey’s martingale.
In the second one, only convergence in law is possible and a different technique is needed. Our results provide a global picture on the long term behavior and corrected a misprint in Pinsky’s paper [Bull. Amer. Math. Soc. 78 (1972), 242-244].
This talk is based on a joint work with Clement Foucart, Chunhua Ma.
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