On emergence times of competition processes - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2011

On emergence times of competition processes

Résumé

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.
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Dates et versions

hal-00595912 , version 1 (25-05-2011)
hal-00595912 , version 2 (03-06-2011)
hal-00595912 , version 3 (08-07-2011)
hal-00595912 , version 4 (15-11-2012)
hal-00595912 , version 5 (23-10-2013)

Identifiants

Citer

Romain Bourget, Loïc Chaumont, Natalia Sapoukhina. On emergence times of competition processes. 2011. ⟨hal-00595912v2⟩
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