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Multivariate generalized Laplace distribution and related random fields

Kozubowski, Tomasz J. ; Podgorski, Krzysztof LU and Rychlik, Igor (2013) In Journal of Multivariate Analysis 113. p.59-72
Abstract
Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Levy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An... (More)
Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Levy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modeling potential of this construction. (C) 2012 Elsevier Inc. All rights reserved. (Less)
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Contribution to journal
publication status
published
subject
keywords
Bessel function distribution, Laplace distribution, Moving average, processes, Stochastic field
in
Journal of Multivariate Analysis
volume
113
pages
59 - 72
publisher
Academic Press
external identifiers
  • wos:000310865300007
  • scopus:84867703621
ISSN
0047-259X
DOI
10.1016/j.jmva.2012.02.010
language
English
LU publication?
yes
id
70baef52-24d4-4539-861e-e031de59e1f5 (old id 3401197)
date added to LUP
2016-04-01 13:10:37
date last changed
2020-09-30 02:36:36
@article{70baef52-24d4-4539-861e-e031de59e1f5,
  abstract     = {Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Levy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modeling potential of this construction. (C) 2012 Elsevier Inc. All rights reserved.},
  author       = {Kozubowski, Tomasz J. and Podgorski, Krzysztof and Rychlik, Igor},
  issn         = {0047-259X},
  language     = {eng},
  pages        = {59--72},
  publisher    = {Academic Press},
  series       = {Journal of Multivariate Analysis},
  title        = {Multivariate generalized Laplace distribution and related random fields},
  url          = {http://dx.doi.org/10.1016/j.jmva.2012.02.010},
  doi          = {10.1016/j.jmva.2012.02.010},
  volume       = {113},
  year         = {2013},
}