Karhunen‐Loève Expansion for the Second Order Detrended Brownian Motion

Yongchun Zhou, Xiaohui Ai, Minghao Lv and Boping Tian

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/457051

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:457051

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