Karhunen-Loeve expansions for the m-th order detrended Brownian motion View Full Text


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Article Info

DATE

2014-10

AUTHORS

XiaoHui Ai, WenBo V. Li

ABSTRACT

The m-th 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 Karhunen-Loeve expansion for the process and establish a connection with the generalized (m-th 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 L2 norm are given. More... »

PAGES

2043-2052

References to SciGraph publications

  • 2011-02. Karhunen-Loève expansions of α-Wiener bridges in CENTRAL EUROPEAN JOURNAL OF MATHEMATICS
  • 1992-01. Comparison results for the lower tail of Gaussian seminorms in JOURNAL OF THEORETICAL PROBABILITY
  • 2005-07. Exact Small Ball Constants for Some Gaussian Processes under the L2-Norm in JOURNAL OF MATHEMATICAL SCIENCES
  • 1988-02. Cholesky decomposition of the Hilbert matrix in JAPAN JOURNAL OF APPLIED MATHEMATICS
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-014-4873-4

    DOI

    http://dx.doi.org/10.1007/s11425-014-4873-4

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1046275878


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