On the hitting times of continuous-state branching processes with immigration

Xan Duhalde; Clément Foucart; Chunhua Ma

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arXiv · 1310.7401

On the hitting times of continuous-state branching processes with immigration

Xan Duhalde·Clément Foucart·Chunhua Ma

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Abstract

We study the two-dimensional joint distribution of the first hitting time of a constant level by a continuous-state branching process with immigration and their primitive stopped at this time. We show an explicit expression of its Laplace transform. Using this formula, we study the polarity of zero and provide a necessary and sufficient criterion for transience or recurrence. We follow the approach of Shiga, T. (1990) [A recurrence criterion for Markov processes of Ornstein-Uhlenbeck type. Probability Theory and Related Fields, 85(4), 425-447], by finding some $λ$-invariant functions for the generator.

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Xan Duhalde, Clément Foucart, Chunhua Ma. 2013-11-22. On the hitting times of continuous-state branching processes with immigration. https://arxiv.org/abs/1310.7401

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