Construction of continuous-state branching processes in varying environments
Probability
2020-03-04 v2
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.
Cite
@article{arxiv.2002.09113,
title = {Construction of continuous-state branching processes in varying environments},
author = {Rongjuan Fang and Zenghu Li},
journal= {arXiv preprint arXiv:2002.09113},
year = {2020}
}