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2020 On the boundary behavior of multi-type continuous-state branching processes with immigration
Martin Friesen, Peng Jin, Barbara Rüdiger
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP364

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 comparison principle for multi-type CBI processes being compared to one-dimensional CBI processes, and then an application of an existing result for one-dimensional CBI processes. The same technique is also used to provide a sufficient condition for the transience of multi-type CBI processes.

Citation

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Martin Friesen. Peng Jin. Barbara Rüdiger. "On the boundary behavior of multi-type continuous-state branching processes with immigration." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP364

Information

Received: 4 February 2019; Accepted: 18 November 2020; Published: 2020
First available in Project Euclid: 24 December 2020

Digital Object Identifier: 10.1214/20-ECP364

Subjects:
Primary: 60G17, 60J25, 60J80

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