ON EMERGENCE TIMES OF COMPETITION PROCESSES

Romain Bourget (1, 2) , Loïc Chaumont (1) , Natalia Sapoukhina (2)

1 LAREMA - Laboratoire Angevin de Recherche en Mathématiques
2 PAVE - INH : Pathologie végétale : biodiversité, écologie, interactions bioagresseurs-plantes

Competition processes are natural extensions of birth-death processes in higher dimensions. At any time, for any type, a birth, a death or a mutation to another type can occur. This work is concerned with the time $S$ at which a particular type emerges in the population through spontaneous birth or mutation. We give some bounds for the tail of the distribution of $S$. Then using properties of quasi-stationary distributions, we give conditions for the existence of an initial law under which $S$ is exponentially distributed. Finally, we provide some examples of applications to the emergence time of pathogen mutants overcoming host resistance in a host-pathogen system.

Mots clés: Competition processes; emergence time; exponential decay; quasi-stationary distribution; host-pathogen system.; host-pathogen system

Domaines: Probabilités [math.PR]

Romain Bourget, Loïc Chaumont, Natalia Sapoukhina. ON EMERGENCE TIMES OF COMPETITION PROCESSES. 2011. ⟨hal-00595912v1⟩