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

## TL;DR

This paper establishes conditions under which multi-type continuous-state branching processes with immigration avoid hitting the boundary, ensuring non-extinction, by comparing them to one-dimensional processes and analyzing their mechanisms.

## Contribution

It provides a new sufficient condition for non-extinction and transience of multi-type CBI processes applicable in any dimension, based on integrability of mechanisms.

## Key findings

- Conditions for non-extinction of multi-type CBI processes.
- Criteria for transience in multi-type CBI processes.
- Extension of one-dimensional results to higher dimensions.

## 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.