On Some Distributional Properties of Subordinated Gaussian Random Fields,Methodology and Computing in Applied Probability

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On Some Distributional Properties of Subordinated Gaussian Random Fields
Methodology and Computing in Applied Probability ( IF 1.0 ) Pub Date : 2022-04-06 , DOI: 10.1007/s11009-022-09958-x
Robin Merkle ₁ , Andrea Barth ₁

Affiliation

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.

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