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Teor. Veroyatnost. i Primenen., 2016, Volume 61, Issue 4, Pages 709–732 (Mi tvp5084)  

This article is cited in 1 scientific paper (total in 1 paper)

How many families survive for a long time?

V. A. Vatutin, E. E. D'yakonova

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Let $\{ Z_{k},k=0,1,\ldots\} $ be a critical branching process in a random environment generated by a sequence of independent and identically distributed random reproduction laws, and 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 $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, random environment, reduced processes, Lévy processes, conditional limit theorems.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005


DOI: https://doi.org/10.4213/tvp5084

Full text: PDF file (326 kB)
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English version:
Theory of Probability and its Applications, 2017, 61:4, 692–711

Bibliographic databases:

Received: 19.08.2016

Citation: V. A. Vatutin, E. E. D'yakonova, “How many families survive for a long time?”, Teor. Veroyatnost. i Primenen., 61:4 (2016), 709–732; Theory Probab. Appl., 61:4 (2017), 692–711

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. G. K. Kobanenko, “Predelnye teoremy dlya ogranichennykh vetvyaschikhsya protsessov”, Diskret. matem., 29:2 (2017), 18–28  mathnet  crossref  elib
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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