English

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}
}