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This article is cited in 2 scientific papers (total in 2 papers)
On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk
V. I. Afanasyev
Abstract:
Let $\{\xi_n\}$ be a critical branching process in a random environment with linear-fractional generating functions, $T$ be the time of extinction of $\{\xi_n\}$, $T_M$ be the first maximum passage time of
$\{\xi_n\}$. We study the asymptotic behaviour of $\mathsf P(T_M>n)$ and prove limit theorems for the random variables $\{T_M/n\mid T>n\}$ and $\{T_M/T\mid T>n\}$ as $n\to\infty$.
Similar results are established for the stopped random walk with zero drift.
Received: 23.12.1998
Citation:
V. I. Afanasyev, “On the time of attaining a maximum by a critical branching process in a random environment and by a stopped random walk”, Diskr. Mat., 12:2 (2000), 31–50; Discrete Math. Appl., 10:3 (2000), 243–264
Linking options:
https://www.mathnet.ru/eng/dm326https://doi.org/10.4213/dm326 https://www.mathnet.ru/eng/dm/v12/i2/p31
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Abstract page: | 495 | Full-text PDF : | 220 | References: | 62 | First page: | 1 |
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