Journal of the
Korean Mathematical Society JKMS

In this paper we establish some results on the increments of a $d$-dimensional Gaussian process with the usual Euclidean norm. In particular we obtain the law of iterated logarithm and the Book-Shore type theorem for the increments of a $d$-dimensional Gaussian process, via estimating upper bounds and lower bounds of large deviation probabilities on the suprema of the $d$-dimensional Gaussian process.

Keywords: Gaussian process, increment, sample path behaviour

MSC numbers: 60F15, 60G15