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

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arxiv 1902.01162 v1 pith:M3TAM5EG submitted 2019-02-04 math.PR

Martin Friesen , Peng Jin , Barbara Rüdiger This is my paper · ORCID
classification math.PR
keywords processesbranchingconditionimmigrationboundarycontinuous-statemulti-typeone-dimensional
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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 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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    math.PR 2019-08 accept novelty 7.0 of 10

    For the anisotropic stable JCIR process, the heat kernel exists and obeys a weighted anisotropic Besov bound, the strong Feller property holds, and in the subcritical case convergence to the invariant measure is expon...

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