On a non-classical invariance principle
Youri Davydov and
Vladimir Rotar
Statistics & Probability Letters, 2008, vol. 78, issue 14, 2031-2038
Abstract:
We consider the invariance principle without the classical condition of asymptotic negligibility of individual terms. More precisely, let r.v.'s {[xi]nj} and {[eta]nj} be such that and the r.v.'s {[eta]nj} are normal. We set Let Xn(t) and Yn(t) be continuous piecewise linear (or polygonal) random functions with vertices at (tkn,Skn) and (tkn,Ykn), respectively, and let Pn and Qn be the respective distributions of the processes Xn(t) and Yn(t) in . The goal of the present paper is to establish necessary and sufficient conditions for convergence of Pn-Qn to zero measure not involving the condition of the asymptotic negligibility of the r.v.'s {[xi]nj} and {[eta]nj}.
Date: 2008
References: View complete reference list from CitEc
Citations: View citations in EconPapers (6)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(08)00074-6
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:78:y:2008:i:14:p:2031-2038
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 ().