Changing the branching mechanism of a continuous state branching process using immigration
Probability
2009-02-13 v2
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.
Keywords
Cite
@article{arxiv.math/0609518,
title = {Changing the branching mechanism of a continuous state branching process using immigration},
author = {Romain Abraham and Jean-Francois Delmas},
journal= {arXiv preprint arXiv:math/0609518},
year = {2009}
}