Sojourns and extremes of Fourier sums and series with random coefficients

Simeon M. Berman

Stochastic Processes and their Applications, 1983, vol. 15, issue 3, 213-238

Abstract: Let X(t) be the trigonometric polynomial [Sigma]kj=0aj(Ut cos jt+Vj sin jt), -[infinity] u}, and M(t) = max{X(s): 0[less-than-or-equals, slant]s[less-than-or-equals, slant]t}. Limit theorems for Lt(u) and P(M(t) > u) for u-->[infinity] are obtained under the hypothesis that the distribution of the random norm ([Sigma]kj=0(U2j+V2j))1 2 belongs to the domain of attraction of the extreme value distribution exp{ e-2}. The results are also extended to the random Fourier series (k=[infinity]).

Keywords: Sojourms; stationary; processes; random; Fourier; series; extremes; random; trigonometric; polynomial; orthogonal; invariance; of; distribution (search for similar items in EconPapers)
Date: 1983
References: Add references at CitEc
Citations: View citations in EconPapers (7)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0304-4149(83)90034-0
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:spapps:v:15:y:1983:i:3:p:213-238

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

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().