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arXiv · 1903.06058

Extinction rate of continuous state branching processes in critical Lévy environments

Vincent Bansaye·Juan Carlos Pardo·Charline Smadi
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Abstract

We study the speed of extinction of continuous state branching processes in a Lévy environment, where the associated Lévy process oscillates. Assuming that the Lévy process satisfies the Spitzer's condition and the existence of some exponential moments, we extend recent results where the associated branching mechanism was stable. Our study relies on the path analysis of the process together with its environment, when this latter is conditioned to have a non negative running infimum. This approach is inspired from the discrete setting with i.i.d. environment studied in (Afanasyev et al. 2005).

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Vincent Bansaye, Juan Carlos Pardo, Charline Smadi. 2021-07-23. Extinction rate of continuous state branching processes in critical Lévy environments. https://arxiv.org/abs/1903.06058

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