On Some Distributional Properties of Subordinated Gaussian Random Fields

Abstract

Motivated by the subordinated Brownian motion, we define a new class of (in general discontinuous) random fields on higher-dimensional parameter domains: the subordinated Gaussian random field. We investigate the pointwise marginal distribution of the constructed random fields, derive a Lévy-Khinchin-type formula and semi-explicit formulas for the covariance function. Further, we study the pointwise stochastic regularity and present various numerical examples.

On properties and applications of Gaussian subordinated Lévy fields

“…The distributional flexibility of the resulting model is, however, again restricted since the stochasticity is governed by the Gaussian field. Another extension of the Gaussian model has been investigated in the recent paper [32]. The construction is motivated by the subordinated Brownian motion, which is a Brownian motion time-changed by a Lévy subordinator (i.e.…”

“…Preliminaries. In the following section, we give a short introduction to Lévy processes and Gaussian random fields following [32] since they are crucial elements for the construction of the Gaussian subordinated Lévy field. For more details we refer the reader to [3,37,6].…”