dc.contributor.author |
Hardy, Robert |
en |
dc.contributor.author |
Harris, Simon |
en |
dc.date.accessioned |
2019-06-19T21:39:15Z |
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dc.identifier.uri |
http://hdl.handle.net/2292/47248 |
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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]. |
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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. |
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dc.rights.uri |
https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm |
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dc.subject |
math.PR |
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dc.subject |
math.PR |
en |
dc.subject |
60J80 |
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dc.title |
Spine proofs for Lp-convergence of branching-diffusion martingales |
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dc.type |
Report |
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dc.rights.holder |
Copyright: The author |
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pubs.author-url |
http://arxiv.org/abs/math/0611056v1 |
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dc.rights.accessrights |
http://purl.org/eprint/accessRights/RestrictedAccess |
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pubs.elements-id |
761976 |
en |
pubs.org-id |
Science |
en |
pubs.org-id |
Statistics |
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pubs.arxiv-id |
math/0611056 |
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pubs.record-created-at-source-date |
2006-11-03 |
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pubs.record-made-public-at-source-date |
2006-11-03 |
en |