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Fractional Laplace motion

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Author

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.

Publishing year

2006

Language

English

Pages

451-464

Publication/Series

Advances in Applied Probability

Volume

38

Issue

2

Document type

Journal article

Publisher

Applied Probability Trust

Topic

  • Probability Theory and Statistics

Keywords

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

Status

Published

ISBN/ISSN/Other

  • ISSN: 0001-8678