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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2013, Volume 282, Pages 231–256
DOI: https://doi.org/10.1134/S0371968513030187 (Mi tm3481) 		 
This article is cited in 13 scientific papers (total in 13 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
Full-text PDF (339 kB) Citations (13)
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DOI: https://doi.org/10.1134/S0371968513030187
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).
Received in December 2012
English version:
Proceedings of the Steklov Institute of Mathematics, 2013, Volume 282, Pages 220–242
DOI: https://doi.org/10.1134/S0081543813060187
Bibliographic databases:
Document Type: Article
UDC: 519.218.27
Language: Russian
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, Trudy Mat. Inst. Steklova, 282, MAIK Nauka/Interperiodica, Moscow, 2013, 231–256; Proc. Steklov Inst. Math., 282 (2013), 220–242
Citation in format AMSBIB
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\paper Evolution of branching processes in a~random environment
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\bookinfo Collected papers. Dedicated to the memory of Boris Aleksandrovich Sevastyanov, corresponding member of the Russian Academy of Sciences
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\vol 282
\pages 231--256
\publ MAIK Nauka/Interperiodica
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  • https://www.mathnet.ru/eng/tm3481
  • https://doi.org/10.1134/S0371968513030187
  • https://www.mathnet.ru/eng/tm/v282/p231
    • This publication is cited in the following 13 articles:
    1. V. A. Vatutin, C. Smadi, “Critical Branching Processes in a Random Environment with Immigration: The Size of the Only Surviving Family”, Proc. Steklov Inst. Math., 316 (2022), 336–355  mathnet  crossref  crossref
    2. V. A. Vatutin, E. E. Dyakonova, “Multitype branching processes in random environment”, Russian Math. Surveys, 76:6 (2021), 1019–1063  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. Smadi Ch., Vatutin V., “Critical Branching Processes in Random Environment With Immigration: Survival of a Single Family”, Extremes, 24:3 (2021), 433–460  crossref  mathscinet  isi
    4. Dong C. Smadi C. Vatutin V.A., “Critical Branching Processes in Random Environment and Cauchy Domain of Attraction”, ALEA-Latin Am. J. Probab. Math. Stat., 17:2 (2020), 877–900  crossref  mathscinet  isi
    5. Bhattacharya A., Palmowski Z., “Slower Variation of the Generation Sizes Induced By Heavy-Tailed Environment For Geometric Branching”, Stat. Probab. Lett., 154 (2019), UNSP 108550  crossref  mathscinet  isi
    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
    8. 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
    9. 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
    10. 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
    11. 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
    12. 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
    13. Elisabeth Bauernschubert, “Recurrence and Transience of Critical Branching Processes in Random Environment with Immigration and an Application to Excited Random Walks”, Adv. Appl. Probab., 46:03 (2014), 687  crossref
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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