Karhunen-Loève Expansion for the Second Order Detrended Brownian Motion

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 t...

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Bibliographic Details
Published inAbstract and Applied Analysis Vol. 2014; no. 2014; pp. 1 - 7
Main Authors Tian, Boping, Lv, Minghao, Ai, Xiaohui, Zhou, Yongchun
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Limiteds 01.01.2014
Hindawi Publishing Corporation
Hindawi Limited
Wiley
Subjects
Brownian motion
Expansion
Gaussian processes
Hilbert space
Mathematical research
Probability
Random variables
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Summary: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.
ISSN:1085-3375
1687-0409
DOI:10.1155/2014/457051