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arXiv · 1902.01162

Boundary behavior of multi-type continuous-state branching processes with immigration

Martin Friesen·Peng Jin·Barbara Rüdiger
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Abstract

In this article we provide a sufficient condition for a continuous-state branching process with immigration (CBI process) to not hit its boundary, i.e. for non-extinction. Our result applies to arbitrary dimension $d \geq 1$ and is formulated in terms of an integrability condition for its immigration and branching mechanisms $F$ and $R$. The proof is based on a suitable comparison with one-dimensional CBI processes and an existing result for one-dimensional CBI processes. The same technique is also used to provide a sufficient condition for transience of multi-type CBI processes.

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Martin Friesen, Peng Jin, Barbara Rüdiger. 2019-02-04. Boundary behavior of multi-type continuous-state branching processes with immigration. https://doi.org/10.1214/20-ecp364

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