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November, 1994 Generalisations of the Bienayme-Galton-Watson Branching Process via its Representation as an Embedded Random Walk
M. P. Quine, W. Szczotka
Ann. Appl. Probab. 4(4): 1206-1222 (November, 1994). DOI: 10.1214/aoap/1177004912

Abstract

We define a stochastic process $\mathscr{X} = \{X_n, n = 0,1,2, \ldots\}$ in terms of cumulative sums of the sequence $K_1, K_2, \ldots$ of integer-valued random variables in such a way that if the $K_i$ are independent, identically distributed and nonnegative, then $\mathscr{X}$ is a Bienayme-Galton-Watson branching process. By exploiting the fact that $\mathscr{X}$ is in a sense embedded in a random walk, we show that some standard branching process results hold in more general settings. We also prove a new type of limit result.

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M. P. Quine. W. Szczotka. "Generalisations of the Bienayme-Galton-Watson Branching Process via its Representation as an Embedded Random Walk." Ann. Appl. Probab. 4 (4) 1206 - 1222, November, 1994. https://doi.org/10.1214/aoap/1177004912

Information

Published: November, 1994
First available in Project Euclid: 19 April 2007

zbMATH: 0820.60069
MathSciNet: MR1304782
Digital Object Identifier: 10.1214/aoap/1177004912

Subjects:
Primary: 60J80
Secondary: 60J10 , 60J15 , 60J99

Keywords: Bienayme-Galton-Watson branching process , embedded random walk , martingale

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.4 • No. 4 • November, 1994
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