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Fractional Poisson Fields

  • Nikolai Leonenko
  • Ely Merzbach
Article

Abstract

Using inverse subordinators and Mittag-Leffler functions, we present a new definition of a fractional Poisson process parametrized by points of the Euclidean space \(\mathbb{R}_+^2\). Some properties are given and, in particular, we prove a long-range dependence property.

Keywords

Poisson fields Long-range dependence Subordinator Inverse subordinator 

AMS 2000 Subject Classifications

60G22 60G60 60G55 

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.School of MathematicsCardiff UniversityCardiffUK
  2. 2.Department of MathematicsBar-Ilan UniversityRamat-GanIsrael

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