Karhunen–Loeve expansions for the detrended Brownian motion

Xiaohui Ai, Wenbo V. Li and Guoqing Liu

Statistics & Probability Letters, 2012, vol. 82, issue 7, 1235-1241

Abstract: The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L2 norm. Distribution identities are established in connection with the second order Brownian bridge developed by MacNeill (1978). As applications, large and small deviation asymptotic behaviors for the L2 norm are given.

Keywords: Detrended Brownian motion; Karhunen–Loeve expansions; Laplace transform; Large deviation; Small deviation (search for similar items in EconPapers)
Date: 2012
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S016771521200079X
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:82:y:2012:i:7:p:1235-1241

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.2012.03.007

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 ().