Abstract
We consider stochastic processes $X=\{X(t),t\in T\}$ represented as a Lévy chaos of finite order, that is, as a finite sum of multiple stochastic integrals with respect to a symmetric infinitely divisible random measure. For a measurable subspace V of $R\sp T$ we prove a very general zero-one law $P(X\in V)=0$ or 1, providing a complete analogue to the corresponding situation in the case of symmetric infinitely divisible processes (single integrals with respect to an infinitely divisible random measure). Our argument requires developing a new symmetrization technique for multi-linear Rademacher forms, as well as generalizing Kanter's concentration inequality to multiple sums.
Citation
Jan Rosiński. Gennady Samorodnitsky. "Symmetrization and concentration inequalities for multilinear forms with applications to zero-one laws for Lévy chaos." Ann. Probab. 24 (1) 422 - 437, January 1996. https://doi.org/10.1214/aop/1042644724
Information