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Title of Journal: Sci China Math

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Abbravation: Science China Mathematics

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Science China Press

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10.1007/s40009-014-0248-1

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1869-1862

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KarhunenLoeve expansions for the Emphasis Type="

Authors: XiaoHui Ai WenBo V Li
Publish Date: 2014/07/14
Volume: 57, Issue: 10, Pages: 2043-2052
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Abstract

The mth order detrended Brownian motion is defined as the orthogonal component of projection of the standard Brownian motion onto the subspace spanned by polynomials of degree up to m We obtain the KarhunenLoeve expansion for the process and establish a connection with the generalized mth order Brownian bridge developed by MacNeill 1978 in the study of distributions of polynomial regression The resulting distribution identity is also verified by a stochastic Fubini approach As applications large and small deviation asymptotic behaviors for the L 2 norm are given

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