Spine proofs for Lp-convergence of branching-diffusion martingales

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dc.contributor.author Hardy, Robert en
dc.contributor.author Harris, Simon en
dc.date.accessioned 2019-06-19T21:39:15Z en
dc.identifier.uri http://hdl.handle.net/2292/47248 en
dc.description.abstract Using 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]. en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher. en
dc.rights.uri https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm en
dc.subject math.PR en
dc.subject math.PR en
dc.subject 60J80 en
dc.title Spine proofs for Lp-convergence of branching-diffusion martingales en
dc.type Report en
dc.rights.holder Copyright: The author en
pubs.author-url http://arxiv.org/abs/math/0611056v1 en
dc.rights.accessrights http://purl.org/eprint/accessRights/RestrictedAccess en
pubs.elements-id 761976 en
pubs.org-id Science en
pubs.org-id Statistics en
pubs.arxiv-id math/0611056 en
pubs.record-created-at-source-date 2006-11-03 en
pubs.record-made-public-at-source-date 2006-11-03 en

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