On convergence rates and the expectation of sums of random variables

R. A. Maller

Stochastic Processes and their Applications, 1978, vol. 8, issue 2, 171-179

Abstract: Let Xi be iidrv's and Sn=X1+X2+...+Xn. When EX21 0 a.s. for some constants [alpha]n. Thus the r.v. Y=supn[greater-or-equal, slanted]1[Sn-[alpha]n-([delta]n log n)1/2]+ is a.s.finite when [delta]>0. We prove a rate of convergence theorem related to the classical results of Baum and Katz, and apply it to show, without the prior assumption EX21 hE(X1-EX1)2, whereas EYh=+[infinity] whenever h>0 and 0

Keywords: Convergence; rates; optimal; stopping; law; of; the; iterated; logarithm (search for similar items in EconPapers)
Date: 1978
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