Spine proofs for Lp-convergence of branching-diffusion martingales

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dc.creatorHardy, Robert
dc.creatorHarris, Simon C.
dc.date2006-11-02
dc.date.accessioned2026-07-07T07:32:27Z
dc.date.available2026-07-07T07:32:27Z
dc.descriptionUsing the foundations laid down in Hardy and Harris (2006) ["A new formulation of the spine approach in branching diffusions", arXiv:math.PR/0611054], we present new spine proofs of the L^p-convergence p>=1) of some key `additive' martingales for three distinct models of branching diffusions, including new results for a multi-type branching Brownian motion and discussion of left-most particle speeds. The spine techniques we develop give clear and simple arguments in the spirit of the conceptual spine proofs found in Kyprianou (2004) ["Travelling wave solutions to the KPP equation, Ann. Inst. H. Poincare Probab. Statist. 40, no.1, pp53-72] and Lyons et al (1997) ["A conceptual proof of the Kesten-Stigum theorem for multi-type branching processes", Classical and modern branching processes, IMA Vol. Math. Appl., vol.84, Springer, New York, pp181-185], and they should also extend to more general classes of branching diffusions. Importantly, the techniques in this paper also pave the way for the path large-deviation results for branching diffusions found in Hardy and Harris (2006) ["A conceptual approach to a path result for branching Brownian motion", Stochastic Processes and their Applications, doi:10.1016/j.spa.2006.05.010].
dc.description26 pages
dc.identifierhttps://arxiv.org/abs/math/0611056
dc.identifierhttp://arxiv.org/abs/math/0611056
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/119119
dc.subjectProbability
dc.subject60J80
dc.titleSpine proofs for Lp-convergence of branching-diffusion martingales
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