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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
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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
2016-04-01 14:59:50
date last changed
2018-11-21 20:32:20
@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}},
  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}},
  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}},
}