L log L criterion for a class of superdiffusions
Rong-Li Liu, Yan-Xia Ren, and Renming Song
Source: J. Appl. Probab. Volume 46, Number 2 (2009), 479-496.
Abstract
In Lyons, Pemantle and Peres (1995), a martingale change of measure method was developed in order to give an alternative proof of the Kesten--Stigum L log L theorem for single-type branching processes. Later, this method was extended to prove the L log L theorem for multiple- and general multiple-type branching processes in Biggins and Kyprianou (2004), Kurtz et al. (1997), and Lyons (1997). In this paper we extend this method to a class of superdiffusions and establish a Kesten--Stigum L log L type theorem for superdiffusions. One of our main tools is a spine decomposition of superdiffusions, which is a modification of the one in Englander and Kyprianou (2004).
Primary Subjects: 60J80, 60F15
Secondary Subjects: 60J25
Keywords: Diffusions; superdiffusions; Poisson point process; Kesten--Stigum theorem; martingale; martingale change of measure
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Permanent link to this document: http://projecteuclid.org/euclid.jap/1245676101
Digital Object Identifier: doi:10.1239/jap/1245676101
Zentralblatt MATH identifier:
05578820
Mathematical Reviews number (MathSciNet):
MR2535827
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