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.
Citation
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
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