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Banach Center Publications

2006 | 72 | 1 | 161-176

Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails

EN

Abstrakty

EN
Two kinds of estimates are presented for tails and moments of random multidimensional chaoses $S = ∑ a_{i₁,..., i_{d}} X_{i₁}^{(1)} ⋯ X_{i_{d}}^{(d)}$ generated by symmetric random variables $X_{i₁}^{(1)},...,X_{i_{d}}^{(d)}$ with logarithmically concave tails. The estimates of the first kind are generalizations of bounds obtained by Arcones and Giné for Gaussian chaoses. They are exact up to constants depending only on the order d. Unfortunately, suprema of empirical processes are involved. The second kind estimates are based on comparison between moments of S and moments of some related Rademacher chaoses. The estimates for pth moment are exact up to a factor $(max(1,ln p))^{d²}$.

161-176

wydano
2006

Twórcy

autor
• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warszawa, Poland
• Department of Mathematical Economics, Warsaw School of Economics, Al. Niepodległości 164, 02-554 Warszawa, Poland