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).
Original language | English (US) |
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Pages (from-to) | 479-496 |
Number of pages | 18 |
Journal | Journal of Applied Probability |
Volume | 46 |
Issue number | 2 |
DOIs | |
State | Published - Jun 2009 |
Keywords
- Diffusions
- Kesten-stigum theorem
- Martingale
- Martingale change of measure
- Poisson point process
- Superdiffusions
ASJC Scopus subject areas
- Statistics and Probability
- General Mathematics
- Statistics, Probability and Uncertainty