Critical Branching Process with Two Types of Particles Evolving in Asynchronous Random Environments

Vladimir Vatutin (1) , Quansheng Liu (2)

1 SMI | RAS - Steklov Mathematical Institute [Moscow]
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique

A two-type pure decomposable branching process in a random environment is considered. Each particle of this process may produce offspring of its own type only. Let $\exp \{X_{k}(i)\}$ be the mean number of children produced by a particle of type $i=1,2$ of generation $k$. Assuming that $X_{k}(2)=-X_{k}(1)$ with probability 1 and that the random walk $S_{n}(1)=X_{1}(1)+\cdots +X_{n}(1)$ specified by the random environment is oscillating, we study the joint conditional distribution of the number of particles in the population at the moments $nt,0

Domaines: Probabilités [math.PR]

Vladimir Vatutin, Quansheng Liu. Critical Branching Process with Two Types of Particles Evolving in Asynchronous Random Environments. Th. Prob. Appl., 2013, 57 (2), pp.279-305. ⟨10.1137/S0040585X97985911⟩. ⟨hal-00909165⟩