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Estimation of moments of sums of independent real random variables. (English) Zbl 0885.60011

Many authors, such as Marcinkiewicz and Zygmund, Burkholder, Rosenthal, have devoted themselves (i.a.) to finding inequalities for the moments of partial sums of independent random variables or martingale differences etc. The present paper proves some new inequalities for sums of independent, symmetric random variables, where the upper and lower bounds are expressed in terms of a special Orlicz norm. As a corollary it follows that the best upper constants \(C_p\) in Rosenthal’s inequality are of the order \(p/ \ln p\).
Reviewer: A.Gut (Uppsala)

MSC:

60E15 Inequalities; stochastic orderings
60G50 Sums of independent random variables; random walks
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