On the Csorgo-Révész increments of finite dimensional Gaussian random fields

Abstract

In this paper, we establish some limit theorems on the combined Csorgo-Révész increments with moduli of continuity for finite dimensional Gaussian random fields under mild conditions, via estimating upper bounds of large deviation probabilities on suprema of the finite dimensional Gaussian random fields.Csorgo-Révész increment; Gaussian process; random field; modulus of continuity; quasi-increasing; regularly varying function; large deviation probability.