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A Comparison Inequality for Sums of Independent Random Variables

✍ Scribed by Stephen J. Montgomery-Smith; Alexander R. Pruss

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
83 KB
Volume
254
Category
Article
ISSN
0022-247X

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✦ Synopsis

We give a comparison inequality that allows one to estimate the tail probabilities of sums of independent Banach space valued random variables in terms of those of independent identically distributed random variables. More precisely, let X 1

X n be independent Banach-valued random variables. Let I be a random variable independent of X 1 X n and uniformly distributed over 1 n . Put X 1 = X I , and let X 2 β€’ β€’ β€’ X n be independent identically distributed copies of X 1 . Then,

for all Ξ» β‰₯ 0, where c is an absolute constant.

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