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Teor. Veroyatnost. i Primenen., 2017, Volume 62, Issue 4, Pages 634–653 (Mi tvp5146)  

This article is cited in 2 scientific papers (total in 2 papers)

Multitype branching processes in random environment: survival probability for the critical case

V. A. Vatutin, E. E. D'yakonova

Novosibirsk State University

Abstract: We investigate the asymptotic behavior of the survival probability of a critical multitype branching process evolving in an environment generated by a sequence of independent identically distributed random variables. Under fairly general assumptions on the form of the offspring generating functions of particles, we show that the probability of survival up to generation $n$ of the process initiated at moment zero by a single particle of type $i$ is equivalent to $\beta_in^{-1/2}$, where $\beta_i$ is a positive constant. This assertion essentially generalizes a number of previously known results.

Keywords: branching processes, random environment, survival probability, change of measure.

Funding Agency Grant Number
Russian Science Foundation 17-11-01173


DOI: https://doi.org/10.4213/tvp5146

Full text: PDF file (457 kB)
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English version:
Theory of Probability and its Applications, 2018, 62:4, 506–521

Bibliographic databases:

Document Type: Article
Received: 30.05.2017

Citation: V. A. Vatutin, E. E. D'yakonova, “Multitype branching processes in random environment: survival probability for the critical case”, Teor. Veroyatnost. i Primenen., 62:4 (2017), 634–653; Theory Probab. Appl., 62:4 (2018), 506–521

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/tvp/v62/i4/p634

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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. E. Le Page, M. Peigné, C. Pham, “The survival probability of a critical multi-type branching process in i.i.d. Random environment”, Ann. Probab., 46:5 (2018), 2946–2972  crossref  mathscinet  isi  scopus
    2. V. Vatutin, V. Wachtel, “Multi-type subcritical branching processes in a random environment”, Adv. Appl. Probab., 50:A (2018), 281–289  crossref  mathscinet  isi  scopus
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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