Branching Processes in Random Environment with Sibling Dependence

Abstract

We consider a population of particles with unit lifetime. Dying, each particle produces offspring whose size depends on the random environment specifying the reproduction law of all particles of the given generation and on the number of relatives of the particle. We study the asymptotic behavior of the survival probability of the population up to a distant moment n under some restrictions on the properties of the environment and family ties and prove a limit theorem for the number of particles in such processes given the respective populations survive for a long time.