A self-normalized Erdos--Rényi type strong law of large numbers

Miklós Csörgo and Qi-Man Shao

Stochastic Processes and their Applications, 1994, vol. 50, issue 2, 187-196

Abstract: The original Erdos--Rényi theorem states that max0[less-than-or-equals, slant]k[less-than-or-equals, slant]n[summation operator]k+[clogn]i=k+1Xi/[clogn]-->[alpha](c),c>0, almost surely for i.i.d. random variables {Xn, n[greater-or-equal, slanted]1} with mean zero and finite moment generating function in a neighbourhood of zero. The latter condition is also necessary for the Erdos--Rényi theorem, and the function [alpha](c) uniquely determines the distribution function of X1. We prove that if the normalizing constant [c log n] is replaced by the random variable [summation operator]k+[clogn]i=k+1(X2i+1), then a corresponding result remains true under assuming only the exist first moment, or that the underlying distribution is symmetric.

Keywords: Erdos--Renyi; strong; laws; p4; self-normalized; increments; of; partial; sums (search for similar items in EconPapers)
Date: 1994
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(94)90117-1
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:50:y:1994:i:2:p:187-196

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().