A class of non-Gaussian second order random fields

Sofia Åberg and Krzysztof Podgórski

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
Non-Gaussian stochastic fields are introduced by means of integrals with respect to independently scattered stochastic measures that have generalized Laplace distributions. In particular, we discuss stationary second order processes that, as opposed to their Gaussian counterpart, have a possibility of accounting for asymmetry and heavier tails. Additionally to this greater flexibility the discussed models continue to share most spectral properties with Gaussian processes. The models extend directly to random fields and thus can be suitable for modeling empirical
data that are used in environmental and engineering sciences. Distributions of spatio-temporal characteristics can be obtained using the generalized Rice formula and effectively computed by numerical methods. The potential for stochastic modeling of real life phenomena that deviate from the Gaussian paradigm is exemplified by a stochastic field model with Matern covariances.
Key words:
spectral density, covariance function, stationary second order processes, Rice formula