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Porträtt av Krzysztof Podgórski. Foto.

Krzysztof Podgórski

Prefekt Statistiska institutionen, Professor

Porträtt av Krzysztof Podgórski. Foto.

Fractional Laplace motion

Författare

  • Tom Kozubowski
  • Mark Meerschaert
  • Krzysztof Podgorski

Summary, in English

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it may also prove useful in modeling financial time series. Its one dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one dimensional distributions are more peaked at the mode than a Gaussian, and their tails are heavier. In this paper, we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

Publiceringsår

2006

Språk

Engelska

Sidor

451-464

Publikation/Tidskrift/Serie

Advances in Applied Probability

Volym

38

Issue

2

Dokumenttyp

Artikel i tidskrift

Förlag

Applied Probability Trust

Ämne

  • Probability Theory and Statistics

Nyckelord

  • infinite divisibility
  • generalized gamma distribution
  • subordination
  • gamma process
  • scaling
  • self-similarity
  • long-range dependence
  • self-affinity
  • fractional Brownian motion
  • Compound process
  • G-type distribution

Aktiv

Published

ISBN/ISSN/Övrigt

  • ISSN: 0001-8678