Karhunen-loève expansion for the second order detrended brownian motion

Yongchun Zhou; Xiaohui Ai; Minghao Lv; Boping Tian

doi:10.1155/2014/457051

Karhunen-loève expansion for the second order detrended brownian motion

Yongchun Zhou
, Xiaohui Ai
, Minghao Lv
, Boping Tian^*

^*Corresponding author for this work

School of Mathematics

Northeast Forestry University
Harbin Institute of Technology

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English
Article number	457051
Journal	Abstract and Applied Analysis
Volume	2014
DOIs	https://doi.org/10.1155/2014/457051
State	Published - 2014

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title = "Karhunen-lo{\`e}ve expansion for the second order detrended brownian motion",

abstract = "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-Lo{\`e}ve 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.",

author = "Yongchun Zhou and Xiaohui Ai and Minghao Lv and Boping Tian",

note = "Publisher Copyright: {\textcopyright} 2014 Yongchun Zhou et al.",

year = "2014",

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AU - Zhou, Yongchun

AU - Ai, Xiaohui

AU - Lv, Minghao

AU - Tian, Boping

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84934932809

U2 - 10.1155/2014/457051

DO - 10.1155/2014/457051

M3 - 文章

AN - SCOPUS:84934932809

SN - 1085-3375

VL - 2014

JO - Abstract and Applied Analysis

JF - Abstract and Applied Analysis

M1 - 457051

ER -

Karhunen-loève expansion for the second order detrended brownian motion

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