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L Log L Criterion for a Class of Superdiffusions
- Source :
- Journal of Applied Probability. 46:479-496
- Publication Year :
- 2009
- Publisher :
- Cambridge University Press (CUP), 2009.
-
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).
- Subjects :
- Statistics and Probability
General Mathematics
010102 general mathematics
Mathematical analysis
01 natural sciences
Combinatorics
010104 statistics & probability
Change of measure
Probability theory
Poisson point process
0101 mathematics
Statistics, Probability and Uncertainty
Martingale (probability theory)
Branching process
Mathematics
Subjects
Details
- ISSN :
- 14756072 and 00219002
- Volume :
- 46
- Database :
- OpenAIRE
- Journal :
- Journal of Applied Probability
- Accession number :
- edsair.doi...........e9fe758f741d4dd68f8054169c6d7159