Construction of continuous-state branching processes in varying environments

Rongjuan Fang; Zenghu Li

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arXiv · 2002.09113

Construction of continuous-state branching processes in varying environments

Rongjuan Fang·Zenghu Li

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Abstract

A continuous-state branching process in varying environments is constructed by the pathwise unique solution to a stochastic integral equation driven by time-space noises. The process arises naturally in the limit theorem of Galton--Watson processes in varying environments established by Bansaye and Simatos (2015). In terms of the stochastic equation we clarify the behavior of the continuous-state process at its bottlenecks, which are the times when it arrives at zero almost surely by negative jumps.

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Rongjuan Fang, Zenghu Li. 2020-02-21. Construction of continuous-state branching processes in varying environments. https://arxiv.org/abs/2002.09113

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