Elena E. Dyakonova

Yaglom Type Limit Theorem for Branching Processes in Random Environment

LetZ n be the number of particlesatmoment n inabranching process in random environment with iid probability generating functions. Imposing Spitzer’s condition on the associated random walk and applying the quenchedapproachwe find the asymptotics of the survival probability of the process up to moment n as n→∞and prove a Yaglom type limit theorem (under appropriate scaling) for Z n conditioned on Z n > 0. 1

Limit Theorems for Reduced Branching Processes in a Random Environment

Let

Extinction of decomposable branching processes

Z(n)

Path to survival for the critical branching processes in a random environment

,

Reduced multitype critical branching processes in random environment

n=0,1,\ldots,

Decomposable branching processes with two types of particles

be a branching process evolving in the random environment generated by a sequence of independent identically distributed generating functions

On subcritical multi-type branching process in random environment

f_{0}(s),f_{1}(s),\ldots,

Waves in Reduced Branching Processes in a Random Environment

and let

Branching processes in random environment

S_{0}=0

Multitype branching processes evolving in i.i.d. random environment: probability of survival for the critical case

,