L log L criterion for a class of superdiffusions
JOURNAL OF APPLIED PROBABILITY(2009)
摘要
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).
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关键词
Diffusions,superdiffusions,Poisson point process,Kesten-Stigum theorem,martingale,martingale change of measure
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