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, 1-7

Abstract:

Based on the norm in the Hilbert Space , 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:457051

DOI: 10.1155/2014/457051

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