Symmetrization and concentration inequalities for multilinear forms with applications to zero-one laws for Lévy chaos
Rosiński, Jan ; Samorodnitsky, Gennady
Ann. Probab., Tome 24 (1996) no. 2, p. 422-437 / Harvested from Project Euclid
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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.
Publié le : 1996-01-14
Classification:  
@article{1042644724,
     author = {Rosi\'nski, Jan and Samorodnitsky, Gennady},
     title = {Symmetrization and concentration inequalities for multilinear
			 forms with applications to zero-one laws for L\'evy chaos},
     journal = {Ann. Probab.},
     volume = {24},
     number = {2},
     year = {1996},
     pages = { 422-437},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1042644724}
}

Rosiński, Jan; Samorodnitsky, Gennady. Symmetrization and concentration inequalities for multilinear
			 forms with applications to zero-one laws for Lévy chaos. Ann. Probab., Tome 24 (1996) no. 2, pp.  422-437. http://gdmltest.u-ga.fr/item/1042644724/