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Convergence of branching processes to the local time of a Bessel process
Author(s) -
Gittenberger Bernhard
Publication year - 1998
Publication title -
random structures and algorithms
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.314
H-Index - 69
eISSN - 1098-2418
pISSN - 1042-9832
DOI - 10.1002/(sici)1098-2418(199810/12)13:3/4<423::aid-rsa12>3.0.co;2-#
Subject(s) - branching process , branching (polymer chemistry) , bessel process , convergence (economics) , bessel function , process (computing) , mathematics , statistical physics , computer science , mathematical analysis , physics , statistics , materials science , economics , orthogonal polynomials , classical orthogonal polynomials , gegenbauer polynomials , composite material , economic growth , operating system
We study Galton–Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence c n tending to infinity as $o(\sqrt{n})$ . It is shown 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. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 13: 423–438, 1998