A class of non-Gaussian second order random fields
Artikel i vetenskaplig tidskrift, 2011

Non-Gaussian stochastic fields are introduced by means of integrals with respect to independently scattered stochastic measures distributed according to generalized Laplace laws. In particular, we discuss stationary second order random fields that, as opposed to their Gaussian counterpart, have a possibility of accounting for asymmetry and heavier tails. Additionally to this greater flexibility the models discussed continue to share most spectral properties with Gaussian processes. Their statistical distributions at crossing levels are computed numerically via the generalized Rice formula. The potential for stochastic modeling of real life phenomena that deviate from the Gaussian paradigm is exemplified by a stochastic field model with Matérn covariances.

infinitely divisible processes


Covariance function

Laplace distribution

Rice formula

Spectral density

second order processes


Sofia Åberg

Chalmers, Matematiska vetenskaper, Matematisk statistik

Göteborgs universitet

K. Podgorski

Lunds universitet


1386-1999 (ISSN) 1572915x (eISSN)

Vol. 14 2 187-222


Sannolikhetsteori och statistik



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