Processus de branchement avec interaction

Vi Le
I2M, Aix-Marseille Université

Date(s) : 17/11/2014   iCal
13 h 30 min - 15 h 30 min

Soutenance de thèse

Branching processes with interaction

This thesis consists of four chapters:

Chapter 1 investigates the distribution of the coalescence time (most recent common ancestor) for two individuals picked at random (uniformly) in the current generation of a continuous time Bienaymé-Galton-Watson process.

In chapter 2 we obtain a Ray-Knight representation of Feller’s branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine in the local time accumulated by H at its current level.

Chapter 3 considers the Feller’s branching diffusion with general competition. We give precise conditions on the competition term, in order to decide whether the extinction time (which is also the height of the process) remains or not bounded as the initial population size tends to infinity, and similarly for the total mass of the process.

In chapter 4 we generalize the results of chapter 3 to the case of continuous state branching process with competition which has discontinuous paths.


*Membres du jury :

Rapporteur du jury : LI ZENGHU
Rapporteur du jury : DHERSIN JEAN-STEPHANE
Membre du jury : LAMBERT AMAURY
Membre du jury : SCHAPIRA BRUNO
Membre du jury : WAKOLBINGER ANTON
Directeur de thèse : PARDOUX ETIENNE


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