Open Access
2014 Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion
Yongchun Zhou, Xiaohui Ai, Minghao Lv, Boping Tian
Abstr. Appl. Anal. 2014: 1-7 (2014). DOI: 10.1155/2014/457051


Based on the norm in the Hilbert Space L2[0,1], the second order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the space spanned by nonlinear function subspace. Karhunen-Loève expansion for this process is obtained together with the relationship of that of a generalized Brownian bridge. As applications, Laplace transform, large deviation, and small deviation are given.


Download Citation

Yongchun Zhou. Xiaohui Ai. Minghao Lv. Boping Tian. "Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion." Abstr. Appl. Anal. 2014 1 - 7, 2014.


Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07022412
MathSciNet: MR3240540
Digital Object Identifier: 10.1155/2014/457051

Rights: Copyright © 2014 Hindawi

Vol.2014 • 2014
Back to Top