Random fields and Gaussian processes constitute fundamental frameworks in modern probability theory and spatial statistics, providing robust tools for modelling complex dependencies over space and ...

Let X = {X(x): x ∊ 𝕊N} be a real-valued, centered Gaussian random field indexed on the N -dimensional unit sphere 𝕊N. Approximations to the excursion probability ℙ{supx∊𝕊N X(x) ≥ u}, as →∞, are ...

CATALOG DESCRIPTION: Fundamentals of random variables; mean-squared estimation; limit theorems and convergence; definition of random processes; autocorrelation and stationarity; Gaussian and Poisson ...

This paper is concerned with everywhere local behaviour of certain classes of random processes which have stationary Gaussian increments. It is shown that for two classes of processes almost all the ...