Generalizing a theorem of Katz

Aurel Spataru

Statistics & Probability Letters, 2010, vol. 80, issue 13-14, 1136-1140

Abstract: The Katz theorem states that if X1,X2,... are i.i.d. random variables, Sn=X1+...+Xn, n>=1, and t>=1, then [summation operator]n>=1nt-2P(Sn>=[epsilon]n) 0, if and only if EX1t =1nt-2P(Sn>=[epsilon]n), [epsilon]>0, when 1 =1, we show that one of these conditions is also necessary.

Keywords: Finitely; inhomogeneous; random; walk; Sums; of; independent; random; variables (search for similar items in EconPapers)
Date: 2010
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(10)00078-7
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:stapro:v:80:y:2010:i:13-14:p:1136-1140

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

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().