This paper treats some 2-dimensional zero-mean stationary Gaussian processes with some long-range dependence and gives the limit theorems for the time spent by those processes in some domains in R2 as an application of the non-central limit theorem.

In this note we settle a question posed by Kasahara, Maejima, and Vervaat. We show that the [alpha]-stable Lévy motion is the only (1/[alpha])-self-similar [alpha]-stable process with stationary increments if 0 [alpha] 1. We also introduce new classes of (1/[alpha])-self-similar...

This paper studies the sample path properties of stochastic processes represented by multiple symmetric [alpha]-stable integrals. It relates the "smoothness" of the sample paths to the "smoothness" of the (non-random) integrand. It also contains results about the behavior of the distribution of...