Zero-One Laws for Multilinear Forms in Gaussian and Other Infinitely Divisible Random Variables

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 of sample paths of stochastic processes represented by multiple integrals.