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Teor. Veroyatnost. i Primenen., 1975, Volume 20, Issue 3, Pages 614–623 (Mi tvp3307)  

This article is cited in 11 scientific papers (total in 11 papers)

Short Communications

Limit distributions of distance to the nearest mutual ancestor

A. M. Zubkov

Moscow

Abstract: Let $\mu(t)$ be the number of particles in a Markov branching process at moment $t$ $(\mu(t)>0, \mu(0)=1)$ and let $t-\tau(t)$ be the moment of division of the last mutual ancestor of all particles existing at moment $t$. We investigate limit distributions of $\tau(t)$ in supercritical, subcritical and critical cases.

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English version:
Theory of Probability and its Applications, 1976, 20:3, 602–612

Bibliographic databases:

Document Type: Article
Received: 10.12.1974

Citation: A. M. Zubkov, “Limit distributions of distance to the nearest mutual ancestor”, Teor. Veroyatnost. i Primenen., 20:3 (1975), 614–623; Theory Probab. Appl., 20:3 (1976), 602–612

Citation in format AMSBIB
\Bibitem{Zub75}
\by A.~M.~Zubkov
\paper Limit distributions of distance to the nearest mutual ancestor
\jour Teor. Veroyatnost. i Primenen.
\yr 1975
\vol 20
\issue 3
\pages 614--623
\mathnet{http://mi.mathnet.ru/tvp3307}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=397915}
\zmath{https://zbmath.org/?q=an:0348.60118}
\transl
\jour Theory Probab. Appl.
\yr 1976
\vol 20
\issue 3
\pages 602--612
\crossref{https://doi.org/10.1137/1120065}


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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. V. A. Vatutin, “Limit theorems for critical Markov branching processes with several types of particles and infinite second moments”, Math. USSR-Sb., 32:2 (1977), 215–225  mathnet  crossref  mathscinet  zmath  isi
    2. Vladimir V., Elena D., “Reduced branching processes in random environment”, Mathematics and Computer Science II - Algorithms, Trees, Combinatorics and Probabilities, Trends in Mathematics, 2002, 455–467  isi
    3. Rahimov I., “Limit theorems for the size of subpopulation of productive individuals”, Stochastic Models, 20:3 (2004), 261–280  crossref  mathscinet  zmath  isi
    4. S. A. Klokov, V. A. Topchii, “Mean fixation time estimates in constant size populations”, Siberian Math. J., 47:6 (2006), 1042–1053  mathnet  crossref  mathscinet  zmath  isi
    5. V. A. Vatutin, E. E. D'yakonova, “Limit theorems for reduced branching processes in a random environment”, Theory Probab. Appl., 52:2 (2008), 277–302  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. V. A. Vatutin, E. E. D'yakonova, “Waves in Reduced Branching Processes in a Random Environment”, Theory Probab. Appl., 53:4 (2009), 679–695  mathnet  crossref  crossref  mathscinet  zmath  isi
    7. 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
    8. V. A. Vatutin, “The structure of decomposable reduced branching processes. I. Finitedimensional distributions”, Theory Probab. Appl., 59:4 (2015), 641–662  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    9. E. E. Dyakonova, “Redutsirovannye mnogotipnye kriticheskie vetvyaschiesya protsessy v sluchainoi srede”, Diskret. matem., 28:4 (2016), 58–79  mathnet  crossref  mathscinet  elib
    10. V. A. Vatutin, E. E. Dyakonova, “Mnogo li semeistv zhivet dolgo?”, Teoriya veroyatn. i ee primen., 61:4 (2016), 709–732  mathnet  crossref  mathscinet  elib
    11. Smadi C. Vatutin V.A., “Reduced Two-Type Decomposable Critical Branching Processes With Possibly Infinite Variance”, Markov Process. Relat. Fields, 22:2 (2016), 311–358  mathscinet  zmath  isi
  • Теория вероятностей и ее применения Theory of Probability and its Applications
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