Acta Mathematica Hungarica
Volume/Issue:
Volume 137: Issue 1-2
A nonclassical LIL for sums of B-valued random variables when extreme terms are excluded
Author: Ke-Ang Fu 1
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  • 1 School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
DOI:
https://doi.org/10.1007/s10474-012-0209-4
Page Count:
1–9
Publication Date:
01 Oct 2012
Online Publication Date:
03 Apr 2012
Article Category:
Research Article
Restricted access

Abstract

Let {X,Xn; n≧1} be a sequence of B-valued i.i.d. random variables. Denote if ∥Xm∥ is the r-th maximum of {∥Xk∥; k≦n}, and let be the trimmed sums, where . Given a sequence of positive constants {h(n), n≧1}, which is monotonically approaching infinity and not asymptotically equivalent to loglogn, a limit result for is derived.

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Cover Acta Mathematica Hungarica
Acta Mathematica Hungarica
Print ISSN:
0236-5294
Online ISSN:
1588-2632
Keywords:
Banach space; nonclassical law of the iterated logarithm; trimmed sums; 60F15; 60G50

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