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Mat. Zametki, 2012, Volume 91, Issue 1, Pages 12–23 (Mi mz8830)  

This article is cited in 3 scientific papers (total in 3 papers)

Total Population Size in Critical Branching Processes in a Random Environment

V. A. Vatutin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: For a critical branching process evolving in a random environment and having geometric distributions of offspring sizes, we study the tail behavior of the distributions of the total size of the population and the maximal number of particles in a generation up to the moment of extinction of the process.

Keywords: branching processes in random environment, offspring number, tail distribution, population size, generating function, random walk, Lévy process

Funding Agency Grant Number
Russian Foundation for Basic Research 08-01-91954


DOI: https://doi.org/10.4213/mzm8830

Full text: PDF file (476 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 91:1, 12–21

Bibliographic databases:

Document Type: Article
UDC: 519.218.2
Received: 16.06.2010

Citation: V. A. Vatutin, “Total Population Size in Critical Branching Processes in a Random Environment”, Mat. Zametki, 91:1 (2012), 12–23; Math. Notes, 91:1 (2012), 12–21

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. Marković, C. Gros, “Power laws and self-organized criticality in theory and nature”, Phys. Rep., 536:2 (2014), 41–74  crossref  mathscinet  adsnasa  isi  scopus
    2. V. A. Vatutin, E. E. D'yakonova, “Multitype branching processes in random environment: survival probability for the critical case”, Theory Probab. Appl., 62:4 (2018), 506–521  mathnet  crossref  crossref  zmath  isi  elib
    3. F. Aurzada, A. Devulder, N. Guillotin-Plantard, F. Pene, “Random walks and branching processes in correlated Gaussian environment”, J. Stat. Phys., 166:1 (2017), 1–23  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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