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

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( √ 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.

• Type: Journal
• Year: 1998
• Where: RSA
• Authors: Bernhard Gittenberger
• Keywords: RSA 1998, Sequence Cn, Total Progeny, Two-sided Three-dimensional Bessel