TY - JOUR

T1 - Orlicz norms of sequences of random variables

AU - Gordon, Yehoram

AU - Litvak, Alexander

AU - Schütt, Carsten

AU - Werner, Elisabeth

PY - 2002/10

Y1 - 2002/10

N2 - Let fi, i = 1, ..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ ℝn the expectation E∥(xifi)i=1n∥N is maximal (up to an absolute constant) if fi, i = 1, ..., n, are independent. In that case we show that the expectation E∥(xi fi)i=1n∥ N is equivalent to ∥x∥M, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.

AB - Let fi, i = 1, ..., n, be copies of a random variable f and let N be an Orlicz function. We show that for every x ∈ ℝn the expectation E∥(xifi)i=1n∥N is maximal (up to an absolute constant) if fi, i = 1, ..., n, are independent. In that case we show that the expectation E∥(xi fi)i=1n∥ N is equivalent to ∥x∥M, for some Orlicz function M depending on N and on distribution of f only. We provide applications of this result.

KW - Orlicz norms

KW - Random variables

UR - http://www.scopus.com/inward/record.url?scp=0036821604&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036821604&partnerID=8YFLogxK

U2 - 10.1214/aop/1039548373

DO - 10.1214/aop/1039548373

M3 - Article

AN - SCOPUS:0036821604

VL - 30

SP - 1833

EP - 1853

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 4

ER -