Karhunen–Loeve expansions for the detrended Brownian motion

Abstract

The detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion into the subspace spanned by linear functions. Karhunen–Loeve expansion for the process is obtained, together with the explicit formula for the Laplace transform of the squared L 2 norm. Distribution identities are established in connection… (More)

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Cite this paper

@inproceedings{Ai2012KarhunenLoeveEF, title={Karhunen–Loeve expansions for the detrended Brownian motion}, author={Xiaohui Ai and Wenbo V. Li and Guoqing Liu}, year={2012} }