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This article is cited in 24 scientific papers (total in 24 papers)
Galton–Watson branching processes in a random environment. II: Finite-dimensional distributions
V. A. Vatutin, E. E. D'yakonova Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
Let $Z_n$ be the number of particles at moment $n$ in a branching process in a random environment. Assuming that $Z_n$ is “critical” in a certain sense we prove theorems describing the asymptotic behavior as $n\to\infty$ of the distribution of the vector $(Z_{[nt_1]},\dots,Z_{[nt_{b}]})$, of the number of particles in the process at moments $0<[nt_1]<\dots<[nt_{b}]=n$ given $ Z_n>0$.
Keywords:
branching processes in random environment, survival probability, limit theorems, critical branching process, random walks, Spitzer condition, stable distributions, joint distributions.
Received: 17.03.2004
Citation:
V. A. Vatutin, E. E. D'yakonova, “Galton–Watson branching processes in a random environment. II: Finite-dimensional distributions”, Teor. Veroyatnost. i Primenen., 49:2 (2004), 231–268; Theory Probab. Appl., 49:2 (2005), 275–309
Linking options:
https://www.mathnet.ru/eng/tvp218https://doi.org/10.4213/tvp218 https://www.mathnet.ru/eng/tvp/v49/i2/p231
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