On probabilities of large deviations in some classes of k-dimensional Borel sets

L. V. Rozovsky

Journal of Multivariate Analysis, 1985, vol. 17, issue 1, 1-26

Abstract: Let X1, X2,..., be a sequence of independent identically distributed random vectors in k-dimensional Euclidean space Rk and let [Phi](A) be the standard normal distribution in Rk, Sn = X1 + ... + Xn. In this paper a behavior of a relation P{1/[radical sign]nSn [set membership, variant] A}/[Phi](A) when set A is contained in some class of Borel sets and [Phi](A) --> 0, n --> [infinity], is investigated. Particularly, the conditions are obtained which are necessary and sufficient for 40 uniformly in all sets A which are the differences between convex Borel sets in Rk satisfying the condition 62 Here [Lambda](z) is a function such that [Lambda](z) [short up arrow] [infinity], [Lambda](z)/z[var epsilon]0 [downwards arrow] 0, 0

Keywords: Large; deviations; independent; random; vectors; convex; sets; normal; distribution (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(85)90091-0
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:jmvana:v:17:y:1985:i:1:p:1-26

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

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().