We characterize the linear and harmonizable fractional stable motions as the self-similar stable processes with stationary increments whose left-equivalent (or right-equivalent) stationary processes are moving averages and harmonizable respectively.

We show that the logarithms of gamma random variables are α-selfdecomposable, and apply the result to show that logarithms of several positive random variables are 1-selfdecomposable.

Two disjoint classes of self similar symmetric stable processes with stationary increments are studied. The first class consists of linear fractional stable processes, which are related to moving average stable processes, and the second class consists of harmonizable fractional stable processes,...

Characterizations of the classes of selfdecomposable (semi-selfdecomposable, resp.) by a stochastic integral with respect to Lévy process (semi-Lévy process, resp.) are known. A similar characterization for the Urbanik-Sato nested subclasses of the class of selfdecomposable distributions is...

We study the rate-of-convergence in the multivariate max-stable limit theorem in terms of various probability metrics.

A class of random matrices whose determinants and some of their powers are infinitely divisible is provided. It includes the right-orthogonally invariant random matrices and mixtures of Wishart matrices.

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.