GENERALISATIONS OF THE BIENAYME-GALTON-WATSON BRANCHING PROCESS VIA ITS REPRESENTATION AS AN EMBEDDED RANDOM WALK
成果类型：
Article
署名作者：
Quine, M. P.; Szczotka, W.
署名单位：
University of Sydney
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1177004912
发表日期：
1994
页码：
1206-1222
关键词：
摘要：
We define a stochastic process H = (X-n = 0, 1, 2, ...) in terms of cumulative sums of the sequence K-1, K-2, ... of integer-valued random variables in such a way that if the K-i, are independent, identically distributed and nonnegative, then H is a Bienayme Galton Watson branching process. By exploiting the fact that H 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.