Second order limit theorems for the Markov branching process in random environments

Limit theorems for subcritical Branching Process in Random Environment depending on the initial number of particles

Asymptotic behaviors for subcritical Branching Processes in Random Environment (BPRE) starting with several particles depend on whether the BPRE is strongly subcritical (SS), intermediate subcritical (IS) or weakly subcritical (WS) (see [12]). Descendances of particles for BPRE are not independent. In the (SS+IS) case, the asymptotic probability of survival is proportional to the initial number...

Ancestral lineages and limit theorems for branching Markov chains

We consider a branching model in discrete time where each individual has a trait in some general state space. Both the reproduction law and the trait inherited by the offsprings may depend on the trait of the mother and the environment. We study the long time behavior of the population and the ancestral lineage of typical individuals under general assumptions, which we specify for applications ...

Central Limit Theorem in Multitype Branching Random Walk

A discrete time multitype (p-type) branching random walk on the real line R is considered. The positions of the j-type individuals in the n-th generation form a point process. The asymptotic behavior of these point processes, when the generation size tends to infinity, is studied. The central limit theorem is proved.

Central limit theorems for a supercritical branching process in a random environment

For a supercritical branching process (Zn) in a stationary and ergodic environment ξ, we study the rate of convergence of the normalized population Wn = Zn/E[Zn|ξ] to its limitW∞: we show a central limit theorem forW∞−Wn with suitable normalization and derive a Berry-Esseen bound for the rate of convergence in the central limit theorem when the environment is independent and identically distrib...

Central and Local Limit Theories in Markov Dependent Random Variables