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Convergence of branching processes to the local time of a Bessel process

✍ Scribed by Bernhard Gittenberger

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 215 KB
Volume: 13
Category: Article
ISSN: 1042-9832
DOI: 10.1002/(sici)1098-2418(199810/12)13:3/4<423::aid-rsa12>3.0.co;2-#

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✦ Synopsis

We study Galton᎐Watson branching processes conditioned on the total ' Ž . progeny to be n which are scaled by a sequence c tending to infinity as o n . It is shown n that this process weakly converges to the total local time of a two-sided three-dimensional Bessel process. This is done by means of characteristic functions and a generating function approach.

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