Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric alpha-stable processes

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dc.creatorHambly, Ben
dc.creatorJones, Liza
dc.date2006-07-14
dc.date.accessioned2026-07-07T07:18:22Z
dc.date.available2026-07-07T07:18:22Z
dc.descriptionSome probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric alpha-stable processes are used to construct new examples of processes which exhibit both divergent and saturating number variance behaviour. We derive a general expression for the number variance for the spatial particle configurations arising from these systems and this enables us to deduce various limiting distribution results for the fluctuations of the associated counting functions. In particular, knowledge of the number variance allows us to introduce and characterize a novel family of centered, long memory Gaussian processes. We obtain fractional Brownian motion as a weak limit of these constructed processes.
dc.identifierhttps://arxiv.org/abs/math/0607345
dc.identifierhttp://arxiv.org/abs/math/0607345
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/114275
dc.subjectProbability
dc.subject60G52, 60G15 (Primary) 60F17, 15A52 (Secondary)
dc.titleNumber variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric alpha-stable processes
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