Karhunen-Loève expansion for the second order detrended Brownian motion
type: Item
instance of: scholarly article
title: Karhunen-Loève expansion for the second order detrended Brownian motion
zbMATH Open document ID: 1469.60257
DOI: 10.1155/2014/457051
author: Y. C. Zhou
author: Xiaohui Ai
author: Minghao Lv
author: Boping Tian
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Based on the norm in the Hilbert space \(L^2 [0, 1]\), 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.
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60G07
zbMATH DE Number: 7022412
zbMATH Keywords: detrended Brownian motion
Wikidata QID: Q59038357
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/457051
OpenAlex ID: W2128148967
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description: scientific article; zbMATH DE number 7022412