Branching Brownian motion: Almost sure growth along unscaled paths

Harris, Simon; Roberts, M

dc.contributor.author	Harris, Simon	en
dc.contributor.author	Roberts, M	en
dc.date.accessioned	2019-06-19T21:39:49Z	en
dc.date.issued	2008-11-11	en
dc.identifier.citation	Arxiv (0811.1704v1). 11 Nov 2008. 20 pages	en
dc.identifier.uri	http://hdl.handle.net/2292/47249	en
dc.description.abstract	We give new results on the growth of the number of particles in a dyadic branching Brownian motion which follow within a fixed distance of a path $f:[0,\infty)\to \mathbb{R}$. We show that it is possible to count the number of particles without rescaling the paths. Our results reveal that the number of particles along certain paths can oscillate dramatically. The methods used are entirely probabilistic, taking advantage of the spine technique developed by, amongst others, Lyons et al, Kyprianou, and Hardy & Harris.	en
dc.relation.ispartof	Arxiv	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.rights.uri	https://arxiv.org/licenses/nonexclusive-distrib/1.0/license.html	en
dc.subject	math.PR	en
dc.subject	math.PR	en
dc.subject	60J80	en
dc.title	Branching Brownian motion: Almost sure growth along unscaled paths	en
dc.type	Report	en
dc.rights.holder	Copyright: The authors	en
pubs.author-url	http://arxiv.org/abs/0811.1704v1	en
dc.rights.accessrights	http://purl.org/eprint/accessRights/OpenAccess	en
pubs.subtype	Working Paper	en
pubs.elements-id	761974	en
pubs.org-id	Science	en
pubs.org-id	Statistics	en
pubs.arxiv-id	0811.1704	en
pubs.number	0811.1704v1	en
pubs.record-created-at-source-date	2019-08-20	en