Processus de branchements dépendant de la densité markovien en temps continu (Density dependent continuous time Markov branching processes) (Q1073464)

The author studies a Markovian, continuous time, two-type branching process, where the off-spring distribution depends on the state of the population. More precisely: If the population contains m individuals of type 1, n of type 2, then at the next death of an individual there will be a random number of off-springs with a distribution, depending on \(m/(m+n)\) and on the type of the predecessor. The lifetimes are assumed to be independent and exponential. The main result gives a sufficient condition for the a.s. convergence of the relative portion of type-1- members in the population, as the time goes to infinity (on the event of non-extinction). The proof is based on convergence results of stochastic algorithms.