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

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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https://hal.archives-ouvertes.fr/hal-00096275
Contributor : Romain Abraham <>
Submitted on : Monday, October 15, 2007 - 11:40:50 AM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Tuesday, September 21, 2010 - 2:16:12 PM

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Romain Abraham, Jean-François Delmas. Changing the branching mechanism of a continuous state branching process using immigration. Annales de l'Institut Henri Poincaré (B) Probabilités et Statistiques, Institute Henri Poincaré, 2009, 45 (1), pp.226-238. ⟨10.1214/07-AIHP165⟩. ⟨hal-00096275v2⟩

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