We establish zero-one laws for non-homogeneous forms of any finite order in Gaussian, non-Gaussian stable, or, more generally, in type G random variables. The random arguments in the form can be decoupled, totally coupled, or only partially coupled. These zero-one laws are applied to the study...

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...

This paper compares the shape of the level sets for two multivariate densities. The densities are positive and continuous, and have the same dependence structure. The density f is heavy-tailed. It decreases at the same rate-up to a positive constant-along all rays. The level sets {fc} for...

We describe several analytical and numerical procedures to obtain bounds on the distribution function of a sum of n dependent risks having fixed overlapping marginals. As an application, we produce bounds on quantile-based risk measures for portfolios of financial and actuarial interest.

Li et al. [Distributions with Fixed Marginals and Related Topics, vol. 28, Institute of Mathematics and Statistics, Hayward, CA, 1996, pp. 198-212] provide bounds on the distribution and on the tail for functions of dependent random vectors having fixed multivariate marginals. In this paper, we...