  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 L\'evy-Khinchin-type
formula and semi-explicit formulas for the covariance function. Further, we
study the pointwise stochastic regularity and validate our theoretical findings
in various numerical examples.
