×

zbMATH — the first resource for mathematics

Measure changes with extinction. (English) Zbl 1163.60309
The authors prove that the inverse of the density of a change of probability measure is only a supermartingale (and not a martingale, as some earlier papers claim...)

MSC:
60G30 Continuity and singularity of induced measures
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Biggins, J.D.; Kyprianou, A.E., Measure change in multitype branching, Adv. appl. probab, 36, 2, 544-581, (2004) · Zbl 1056.60082
[2] Durrett, R., Probability: theory and examples, (2004), Duxbury Press Belmont, CA
[3] Engländer, J.; Kyprianou, A.E., Local extinction versus local exponential growth for spatial branching processes, Ann. probab., 32, 1A, 78-99, (2004) · Zbl 1056.60083
[4] Hardy, R., Harris, S.C., 2009. A spine approach to branching diffusions with applications to \(\mathcal{L}^p\)-convergence of martingales. Séminaire de Probabilités, XLII (in press) · Zbl 1193.60100
[5] Harris, S.C., Roberts, M.I., 2008. Branching Brownian motion: Almost sure growth along unscaled paths. Preprint http://arxiv.org/abs/0811.1704
[6] Kuhlbusch, D., On weighted branching processes in random environment, Stoch. process. appl., 109, 1, 113-144, (2004) · Zbl 1075.60111
[7] Lyons, R., A simple path to biggins’ martingale convergence for branching random walk, (), 217-221 · Zbl 0897.60086
[8] Williams, D., Probability with martingales, (1991), Cambridge University Press Cambridge, UK · Zbl 0722.60001
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.