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Diskr. Mat., 1998, Volume 10, Issue 1, Pages 141–157 (Mi dm405)  

This article is cited in 13 scientific papers (total in 13 papers)

Limit theorems for a moderately subcritical branching process in a random environment

V. I. Afanasyev


Abstract: Let $\{\xi_n\}$ be a moderately subcritical branching process in a random environment with linear-fractional generating functions, $m_n$ be the conditional expectation of $\xi_n$ with respect to the random environment. We prove theorems on convergence of the sequence of random processes
$$ \{\xi_{[nt]}/m_{[nt]}, t\in(0,1)\mid \xi_n>0\} $$
as $n\to\infty$ in distribution, and of the initial and final segments of the random sequence $\xi_0/m_0,\xi_1/m_1,\ldots,\xi_n/m_n$ considered under the condition that $\{\xi_n>0\}$.

DOI: https://doi.org/10.4213/dm405

Full text: PDF file (1200 kB)

English version:
Discrete Mathematics and Applications, 1998, 8:1, 35–52

Bibliographic databases:

UDC: 519.2
Received: 10.03.1997

Citation: V. I. Afanasyev, “Limit theorems for a moderately subcritical branching process in a random environment”, Diskr. Mat., 10:1 (1998), 141–157; Discrete Math. Appl., 8:1 (1998), 35–52

Citation in format AMSBIB
\Bibitem{Afa98}
\by V.~I.~Afanasyev
\paper Limit theorems for a moderately subcritical branching process in a random environment
\jour Diskr. Mat.
\yr 1998
\vol 10
\issue 1
\pages 141--157
\mathnet{http://mi.mathnet.ru/dm405}
\crossref{https://doi.org/10.4213/dm405}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1669043}
\zmath{https://zbmath.org/?q=an:0977.60080}
\transl
\jour Discrete Math. Appl.
\yr 1998
\vol 8
\issue 1
\pages 35--52


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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. Fleischmann K., Vatutin V.A., “Reduced subcritical Galton-Watson processes in a random environment”, Advances in Applied Probability, 31:1 (1999), 88–111  crossref  mathscinet  zmath  isi  scopus
    2. V. I. Afanasyev, “Limit theorems for an intermediately subcritical and a strongly subcritical branching process in a random environment”, Discrete Math. Appl., 11:2 (2001), 105–131  mathnet  crossref  mathscinet  zmath
    3. V. I. Afanasyev, “A functional limit theorem for a critical branching process in a random environment”, Discrete Math. Appl., 11:6 (2001), 587–606  mathnet  crossref  mathscinet  zmath
    4. Geiger J., Kersting G., Vatutin V.A., “Limit theorems for subcritical branching processes in random environment”, Annales de l Institut Henri Poincare-Probabilites et Statistiques, 39:4 (2003), 593–620  crossref  mathscinet  zmath  adsnasa  isi  scopus
    5. V. A. Vatutin, “Limit theorem for an intermediate subcritical branching process in a random environment”, Theory Probab. Appl., 48:3 (2004), 481–492  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Vatutin V., Zheng X., “Subcritical Branching Processes in a Random Environment Without the Cramer Condition”, Stoch. Process. Their Appl., 122:7 (2012), 2594–2609  crossref  mathscinet  zmath  isi  elib  scopus
    7. Afanasyev V.I., Boeinghoff C., Kersting G., Vatutin V.A., “Limit Theorems for Weakly Subcritical Branching Processes in Random Environment”, J. Theor. Probab., 25:3 (2012), 703–732  crossref  mathscinet  zmath  isi  scopus
    8. V. A. Vatutin, E. E. Dyakonova, S. Sagitov, “Evolution of branching processes in a random environment”, Proc. Steklov Inst. Math., 282 (2013), 220–242  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. Vatutin V., “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
    10. Bansaye V., Vatutin V., “On the survival probability for a class of subcritical branching processes in random environment”, Bernoulli, 23:1 (2017), 58–88  crossref  mathscinet  zmath  isi  elib  scopus
    11. Grama I., Lauvergnat R., Le Page E., “The Survival Probability of Critical and Subcritical Branching Processes in Finite State Space Markovian Environment”, Stoch. Process. Their Appl., 129:7 (2019), 2485–2527  crossref  isi
    12. V. A. Vatutin, E. E. D'yakonova, “Multitype weakly subcritical branching processes in random environment”, Discrete Math. Appl., 31:3 (2021), 207–222  mathnet  crossref  crossref  mathscinet  isi  elib
    13. V. A. Vatutin, E. E. D'yakonova, “The initial evolution stage of a weakly subcrtical branching process in a random environment”, Theory Probab. Appl., 64:4 (2020), 535–552  mathnet  crossref  crossref  mathscinet  isi  elib
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