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

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 $d\ge 1$ 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.

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• Existence of densities for stochastic differential equations driven by Lévy processes with anisotropic jumps
• Stochastic equation and exponential ergodicity in Wasserstein distances for affine processes
• Affine Jump-Diffusions: Stochastic Stability and Limit Theorems
• Existence of limiting distribution for affine processes
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Cited by in corpus (2)

• Existence of densities for multi-type CBI processes
• On the anisotropic stable JCIR process