  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.
