How many families survive for a long time

Abstract

A critical branching process $\left\{Z_k,k=0,1,2,...\right\}$ in a random environment generated by a sequence of independent and identically distributed random reproduction laws is considered.\ Let $Z_{p,n}$ be the number of particles at time $p\le n$ having a positive offspring number at time $n$. \ A theorem is proved describing the limiting behavior, as of the distribution of a properly scaled process $\log Z_{p,n}$ under the assumptions $Z_n>0$ and $p\ll n$.

arXiv admin note: text overlap with arXiv:1603.03199

References in corpus (1)

• Invariance principles for random walks conditioned to stay positive