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Tr. Mat. Inst. Steklova, 2013, Volume 282, Pages 231–256 (Mi tm3481)  

This article is cited in 7 scientific papers (total in 7 papers)

Evolution of branching processes in a random environment

V. A. Vatutina, E. E. Dyakonovaa, S. Sagitovb

a Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow, Russia
b Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Gothenburg, Sweden

Abstract: This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in independent and identically distributed random environments. This is a natural generalization of the time-inhomogeneous branching processes. The key assumptions of the family of population models in question are nonoverlapping generations and discrete time. The reader should be aware of the fact that there are many very interesting papers covering other issues in the theory of branching processes in random environments which are not mentioned here.

Funding Agency Grant Number
Russian Foundation for Basic Research 11-01-00139
Swedish Research Council 621-2010-5623
This work was supported by the Russian Foundation for Basic Research (project no. 11-01-00139) and by the Swedish Research Council (project no. 621-2010-5623).


DOI: https://doi.org/10.1134/S0371968513030187

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English version:
Proceedings of the Steklov Institute of Mathematics, 2013, 282, 220–242

Bibliographic databases:

Document Type: Article
UDC: 519.218.27
Received in December 2012

Citation: V. A. Vatutin, E. E. Dyakonova, S. Sagitov, “Evolution of branching processes in a random environment”, Branching processes, random walks, and related problems, Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences, Tr. Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 231–256; Proc. Steklov Inst. Math., 282 (2013), 220–242

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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. Bauernschubert, “Recurrence and transience of critical branching processes in random environment with immigration and an application to excited random walks”, Adv. in Appl. Probab., 46:3 (2014), 687–703  crossref  mathscinet  zmath  isi  scopus
    2. V. A. Vatutin, E. E. D'yakonova, “How many families survive for a long time?”, Theory Probab. Appl., 61:4 (2017), 692–711  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. Vatutin, “Subcritical branching processes in random environment”, Branching Processes and Their Applications, Lecture Notes in Statistics, 219, ed. DelPuerto I. Gonzalez M. Gutierrez C. Martinez R. Minuesa C. Molina M. Mota M. Ramos A., Springer, 2016, 97–115  crossref  mathscinet  zmath  isi  scopus
    4. 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
    5. V. Vatutin, E. Dyakonova, “Path to survival for the critical branching processes in a random environment”, J. Appl. Probab., 54:2 (2017), 588–602  crossref  mathscinet  isi  scopus
    6. Z. Li, W. Xu, “Asymptotic results for exponential functionals of Levy processes”, Stoch. Process. Their Appl., 128:1 (2018), 108–131  crossref  mathscinet  zmath  isi  scopus
    7. B. J. Pichugin, N. V. Pertsev, V. A. Topchii, K. K. Loginov, “Stochastic modelling of age-structured population with time and size dependence of immigration rate”, Russ. J. Numer. Anal. Math. Model, 33:5 (2018), 289–299  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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