-dimensional vectors of regression coefficients. For several model terms, such as penalised splines or Markov random fields, these Gaussian …

random fields indexed by <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb {Z …

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields … under natural and easily verifiable conditions. More precisely, we deal with random fields of the form Xk=g(εk−s,s∈Zd), k … framework for stationary ergodic random fields. Under a short-range dependence condition, we show that the central limit theorem …

We present two new classes of stationary max-stable random fields. For the first class, we use the spectral … distributions of both max-stable random fields and give sufficient conditions for the sample paths to be γ-Hölder continuous … of Rd to construct new max-stable random fields. We provide explicit expressions for the pairwise distribution function. …