Continuous state branching processes in random environment: The Brownian case

S. Palau and J.C. Pardo

Stochastic Processes and their Applications, 2017, vol. 127, issue 3, 957-994

Abstract: We consider continuous-state branching processes that are perturbed by a Brownian motion. These processes are constructed as the unique strong solution of a stochastic differential equation. The long-term behaviours are studied. In the stable case, the extinction and explosion probabilities are given explicitly. We find three regimes for the asymptotic behaviour of the explosion probability and five regimes for the asymptotic behaviour of the extinction probability. In the supercritical regime, the process conditioned on eventual extinction has three regimes for the asymptotic behaviour of the extinction probability. Finally, the process conditioned on non-extinction and the process with immigration are given.

Keywords: Continuous state branching processes in random environment; Brownian motion; Explosion and extinction probabilities; Exponential functional of Brownian motion; Q-process; Supercritical process conditioned on eventual extinction; Continuous state branching processes with immigration in random environment (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:127:y:2017:i:3:p:957-994

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DOI: 10.1016/j.spa.2016.07.006

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