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

  title={Number variance from a probabilistic perspective: infinite systems of independent Brownian motions and symmetric -stable processes.},
  author={Ben M. Hambly and L. A. Jones},
  journal={arXiv: Probability},
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… 
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