Electronic Communications in Probability

On the boundary behavior of multi-type continuous-state branching processes with immigration

Martin Friesen, Peng Jin, and 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 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.

Article information

Source
Electron. Commun. Probab., Volume 25 (2020), paper no. 84, 14 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1608779421

Digital Object Identifier
doi:10.1214/20-ECP364

Subjects
Primary: 60G17: Sample path properties 60J25: Continuous-time Markov processes on general state spaces 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Keywords
multi-type continuous-state branching process with immigration extinction transience comparison principle

Rights
Creative Commons Attribution 4.0 International License.

Citation

Friesen, Martin; Jin, Peng; Rüdiger, Barbara. On the boundary behavior of multi-type continuous-state branching processes with immigration. Electron. Commun. Probab. 25 (2020), paper no. 84, 14 pp. doi:10.1214/20-ECP364. https://projecteuclid.org/euclid.ecp/1608779421


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