In this paper, we investigate several sample path properties on the increments of (N,d)-Gaussian random fields and also we obtain the law of iterated logarithm for the Gaussian random field, via estimating upper and lower bounds of large deviation probabilities on suprema of the (N,d)- Gaussian...

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...

Let be a centered strictly stationary Gaussian random field, where is the d-dimensional lattice of all points in d-dimensional Euclidean space having nonnegative integer coordinates. Put Sn=[summation operator]0[less-than-or-equals, slant]j[less-than-or-equals, slant]n[xi]j for and...

In this paper, we study path properties of a d-dimensional Gaussian process with the usual Euclidean norm, via estimating upper bounds of large deviation probabilities on the suprema of the Gaussian process.

We derive the invariance principle for the linear random field generated by identically distributed and associated random fields. Our result extends the result in Bulinski and Keane [Bulinski, A.V., Keane, M.S., 1996. Invariance principle for associated random fields. J. Math. Sci. 81,...