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

• Autorzy: Rafał M. Łochowski
• Języki publikacji: 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 $(max(1,ln p))^{d²}$.

Kategorie tematyczne

• 60E15: Inequalities; stochastic orderings

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2006
• Tom: 72
• Numer: 1
• Strony: 161-176

Daty

wydano

2006

Twórcy

autor

Rafał M. Łochowski

• 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

Identyfikatory

DOI

10.4064/bc72-0-11