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Changing the branching mechanism of a continuous state branching process using immigration

Romain Abraham·Jean-Francois Delmas
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Abstract

We construct a continuous state branching process with immigration (CBI) whose immigration depends on the CBI itself and we recover a continuous state branching process (CB). This provides a dual construction of the pruning at nodes of CB introduced by the authors in a previous paper. This construction is a natural way to model neutral mutation. Using exponential formula, we compute the probability of extinction of the original type population in a critical or sub-critical quadratic branching, conditionally on the non extinction of the total population.

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Romain Abraham, Jean-Francois Delmas. 2007-10-15. Changing the branching mechanism of a continuous state branching process using immigration. https://doi.org/10.1214/07-aihp165

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