Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails
Rafał M. Łochowski
Banach Center Publications, Tome 72 (2006), p. 161-176 / Harvested from The Polish Digital Mathematics Library
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Two kinds of estimates are presented for tails and moments of random multidimensional chaoses S=∑ai₁,...,idXi₁(1)⋯Xid(d) generated by symmetric random variables Xi₁(1),...,Xid(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,lnp))d².

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:282330 
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     author = {Rafa\l\ M. \L ochowski},
     title = {Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails},
     journal = {Banach Center Publications},
     volume = {72},
     year = {2006},
     pages = {161-176},
     zbl = {1105.60018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-11}
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Rafał M. Łochowski. Moment and tail estimates for multidimensional chaoses generated by symmetric random variables with logarithmically concave tails. Banach Center Publications, Tome 72 (2006) pp. 161-176. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc72-0-11/