Multivariate generalized Laplace distribution and related random fields
Journal article, 2013

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.

Laplace distribution



Moving average processes

Stochastic field

Bessel function distribution


T. J. Kozubowski

University of Nevada, Reno

K. Podgorski

Lund University

Igor Rychlik

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Journal of Multivariate Analysis

0047-259X (ISSN) 1095-7243 (eISSN)

Vol. 113 Special Issue: SI 59-72

Subject Categories

Probability Theory and Statistics



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