Strong laws for sequences in the vicinity of the LIL

Allan Gut and Ulrich Stadtmüller

Statistics & Probability Letters, 2017, vol. 122, issue C, 63-72

Abstract: The present paper is devoted to strong laws of large numbers under moment conditions near those of the law of the iterated logarithm (LIL) for i.i.d sequences. More precisely, we wish to investigate possible limit theorems under moment conditions which are stronger than p for any p<2, in which case we know that there is a.s. convergence to 0, and weaker than EX2<∞, in which case the LIL holds.

Keywords: Sums of independent, identically distributed random variables; The law of the iterated logarithm; The strong law of large numbers; Borel–Cantelli lemmas; Exponential bounds (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715216302267
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:122:y:2017:i:c:p:63-72

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

DOI: 10.1016/j.spl.2016.10.027

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 ().