How many families survive for a long time

V. A. Vatutin; E. E. Dyakonova

How many families survive for a long time

Probability 2016-08-30 v1

Authors: V. A. Vatutin , E. E. Dyakonova

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 $p\leq n$ having a positive offspring number at time $n$ . \ A theorem is proved describing the limiting behavior, as $% n\rightarrow \infty$ of the distribution of a properly scaled process $\log Z_{p,n}$ under the assumptions $Z_{n}>0$ and $p\ll n$ .

Keywords

branching processes coalescent theory ruin theory

Cite

@article{arxiv.1608.08062,
  title  = {How many families survive for a long time},
  author = {V. A. Vatutin and E. E. Dyakonova},
  journal= {arXiv preprint arXiv:1608.08062},
  year   = {2016}
}

Comments

arXiv admin note: text overlap with arXiv:1603.03199

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