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Abstract: We study Galton-Watson branching processes conditioned on the total progeny to be n which are scaled by a sequence cn tending to infinity as o( p n). It is shown that this process weakly converges to the totallocal time of a two-sided three-dimensional Bessel process. This is done by means of characteristic functions and a generating function approach. 1. (Update)
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BibTeX entry: (Update)
@article{ gittenberger98convergence,
author = "Bernhard Gittenberger",
title = "Convergence of branching processes to the local time of a Bessel process",
journal = "Random Structures and Algorithms",
volume = "13",
number = "3-4",
pages = "423-438",
year = "1998",
url = "citeseer.ist.psu.edu/500154.html" }
Citations (may not include all citations):602 Convergence of Probability Measures (context) - Billingsley - 1968
294 Brownian Motion and Stochastic Calculus (context) - Karatzas, Shreve - 1988
234 Continuous Martingales and Brownian Motion (context) - Revuz, Yor - 1991
151 Singularity analysis of generating functions (context) - Flajolet, Odlyzko - 1990
66 the altitude of nodes in random trees (context) - Meir, Moon - 1978
42 The continuum random tree II: an overview (context) - Aldous - 1991
32 Markov Processes (context) - Williams - 1979
22 Optimization Software (context) - Kolchin, Mappings - 1986
21 Marking in combinatorial constructions: generating functions.. (context) - Drmota, Soria - 1995
20 of random trees, Random Structures and Algorithms (context) - Drmota, Gittenberger et al. - 1997
18 The SDE solved by local times of a Brownian excursion or bri.. - Pitman - 1997
15 Excursions of Brownian motion and Bessel processes (context) - Getoor, Sharpe - 1979
12 The asymptotic contour process of a binary tree is a Brownia.. (context) - Gutjahr, Ch - 1992
11 the contour of random trees - Gittenberger
8 The Galton-Watson process conditioned on the total progeny (context) - Kennedy - 1975
7 Strata of random mappings -- a combinatorial approach - Drmota, Gittenberger
7 Analytic Functions (context) - Evgrafov - 1966
4 Correlations on the strata of a random mapping (context) - Drmota - 1995
2 Conditioned branching processes and their limiting diffusion.. (context) - Lamperti, Ney - 1968
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