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Multifractional Probabilistic Laws

  • M. D. Ruiz-Medina
  • J. M. Angulo
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Part of the Statistics for Industry and Technology book series (SIT)

Abstract

In this paper, we apply the theory of pseudodifferential operators and Sobolev spaces to characterize fractional and multifractional probability densities. In the fractional case, local regularity properties of the probability density function are given in terms of fractional moment conditions satisfied by the characteristic function. Conversely, the parameter defining the order of the fractional Sobolev space where the characteristic function lies provides the index of stability in relation to fractional moment conditions of the probability density. The extension to the multifractional case leads to the introduction of new probabilistic models considering the theory of pseudodifferential operators and fractional Sobolev spaces of variables order.

Keywords and pharases

Bessel distribution fractional pseudodifferential operators Laplace distribution multifractional pseudodifferential operators 

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Copyright information

© Birkhäuser Boston 2006

Authors and Affiliations

  • M. D. Ruiz-Medina
    • 1
  • J. M. Angulo
    • 1
  1. 1.University of GranadaGranadaSpain

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