On the renewal measure for Gaussian sequences

Fima C. Klebaner

Statistics & Probability Letters, 1986, vol. 4, issue 4, 167-171

Abstract: A form for U(t), the expected number of times a Gaussian sequence falls below a level of t, is given in terms of the mean M(x) and the variance V2(x) functions. It is shown that under general conditions U(t) ~ M(-1)(t), t --> [infinity]. Moreover, if M and V are regularly varying at infinity functions, then U(t) - M(-1)(t) is also regularly varying at infinity. A renewal theorem for stationary Gaussian sequences is given, where it is shown that the asymptotic behavior of U(t) - t/[mu] is determined by the asymptotic behavior of V2(t)/t.

Keywords: renewal; theorem; Gaussian; sequence; stationary; sequence (search for similar items in EconPapers)
Date: 1986
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0167-7152(86)90060-X
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:4:y:1986:i:4:p:167-171

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 ().