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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
Full Text:
##### 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
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