Zero-one laws for multilinear forms in Gaussian and other infinitely divisible random variables

Jan Rosinski
Gennady Samorodnitsky
Murad S. Taqqu

Abstract:

We establish zero-one laws for non-homogeneous forms of any finite order in Gaussian, non-Gausian 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 of sample paths of stochastic processes represented by multiple integrals.