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• W2950184414 abstract "Some probabilistic aspects of the number variance statistic are investigated. Infinite systems of independent Brownian motions and symmetric -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." @default.
• W2950184414 created "2019-06-27" @default.
• W2950184414 creator A5065589370 @default.
• W2950184414 creator A5071306417 @default.
• W2950184414 date "2006-07-14" @default.
• W2950184414 modified "2023-09-27" @default.
• W2950184414 title "Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes." @default.
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• W2950184414 hasPublicationYear "2006" @default.
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