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Skewed Laplace distributions II: divisibility properties and extensions to stochastic processes.

Kozubowski, Tomasz and Podgorski, Krzysztof LU (2008) In Mathematical Scientist 33(1).
Abstract
This paper is a continuation of cite{KP06}, where we discussed the origins and inter-relations of major types of skew Laplace distributions. Here, we review the properties of classical and geometric infinite divisibility as well as self-decomposability, which are crucial in extending univariate Laplace models to stochastic processes. General schemes based on these properties lead to several new non-Gaussian stationary autoregressive processes and continuous-time L'evy processes having potential use in stochastic modeling.
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author
organization
publishing date
type
Contribution to journal
publication status
in press
subject
keywords
Mittag-Leffler distribution, non-Gaussian time series model, Linnik distribution, L'evy process, infinite divisibility, geometric summation, geometric infinite divisibility, class L, bilateral exponential law, autoregressive process, Asymmetric Laplace law, self decomposable law, variance-gamma process, skew double-exponential model
in
Mathematical Scientist
volume
33
issue
1
publisher
Applied Probability Trust
ISSN
0312-3685
language
English
LU publication?
yes
id
0f598e9b-ea8d-4d4e-9f0d-e5b3bec11441 (old id 839289)
date added to LUP
2008-01-10 14:52:52
date last changed
2016-04-16 02:29:36
@article{0f598e9b-ea8d-4d4e-9f0d-e5b3bec11441,
  abstract     = {This paper is a continuation of cite{KP06}, where we discussed the origins and inter-relations of major types of skew Laplace distributions. Here, we review the properties of classical and geometric infinite divisibility as well as self-decomposability, which are crucial in extending univariate Laplace models to stochastic processes. General schemes based on these properties lead to several new non-Gaussian stationary autoregressive processes and continuous-time L'evy processes having potential use in stochastic modeling.},
  author       = {Kozubowski, Tomasz and Podgorski, Krzysztof},
  issn         = {0312-3685},
  keyword      = {Mittag-Leffler distribution,non-Gaussian time series model,Linnik distribution,L'evy process,infinite divisibility,geometric summation,geometric infinite divisibility,class L,bilateral exponential law,autoregressive process,Asymmetric Laplace law,self decomposable law,variance-gamma process,skew double-exponential model},
  language     = {eng},
  number       = {1},
  publisher    = {Applied Probability Trust},
  series       = {Mathematical Scientist},
  title        = {Skewed Laplace distributions II: divisibility properties and extensions to stochastic processes.},
  volume       = {33},
  year         = {2008},
}