M. González Velasco, P. Martín-Chávez, I. M. del Puerto García

Firstly, the continuous state branching processes arose from limit processes of rescaled Bienaymé-Galton-Watson (BGW) processes. A controlled branching process (CBP) is a modification of the standard BGW process in which the number of progenitors in each generation is determined by a random mechanism. It is the aim of this talk to research the limit of the rescaled controlled branching processes. In particular, we consider a CBP starting from a random number of initial individuals and provide a Feller diffusion approximation for rescaled critical CBPs making use of limit theorems for random step processes.

This research has been supported by the Junta de Extremadura (grant GR21050) and by grant PID2019-108211GB-I00 funded by MCIN/AEI/10.13039/501100011033, by “ERDF A way of making Europe”.

Keywords: Controlled branching process, diffusion process, random step process, limit result


GT17 Stochastic Processes and their Applications I
June 7, 2022  12:00 PM

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