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

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 >= 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.