Fractional Laplace motion
(2006) In Advances in Applied Probability 38(2). p.451-464- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/938211
- author
- Kozubowski, Tom ; Meerschaert, Mark and Podgorski, Krzysztof LU
- publishing date
- 2006
- type
- Contribution to journal
- publication status
- published
- subject
- 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
- in
- Advances in Applied Probability
- volume
- 38
- issue
- 2
- pages
- 451 - 464
- publisher
- Applied Probability Trust
- external identifiers
-
- scopus:33745963004
- ISSN
- 0001-8678
- language
- English
- LU publication?
- no
- id
- 271524b4-d831-4396-bcb1-b32cd728e22d (old id 938211)
- date added to LUP
- 2016-04-01 12:18:09
- date last changed
- 2022-04-13 17:11:39
@article{271524b4-d831-4396-bcb1-b32cd728e22d,
abstract = {{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.}},
author = {{Kozubowski, Tom and Meerschaert, Mark and Podgorski, Krzysztof}},
issn = {{0001-8678}},
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}},
language = {{eng}},
number = {{2}},
pages = {{451--464}},
publisher = {{Applied Probability Trust}},
series = {{Advances in Applied Probability}},
title = {{Fractional Laplace motion}},
volume = {{38}},
year = {{2006}},
}