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A note on Karhunen–Loève expansions for the demeaned stationary Ornstein–Uhlenbeck process

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  • Ai, Xiaohui

Abstract

In this paper we obtain the Karhunen–Loève expansion and distribution identity for the demeaned stationary Ornstein–Uhlenbeck process. Some applications are given to small deviation asymptotic behavior for the L2 norm and Laplace transform for the process.

Suggested Citation

  • Ai, Xiaohui, 2016. "A note on Karhunen–Loève expansions for the demeaned stationary Ornstein–Uhlenbeck process," Statistics & Probability Letters, Elsevier, vol. 117(C), pages 113-117.
    • Handle: RePEc:eee:stapro:v:117:y:2016:i:c:p:113-117
    DOI: 10.1016/j.spl.2016.05.017
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    References listed on IDEAS

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    1. Ai, Xiaohui & Li, Wenbo V. & Liu, Guoqing, 2012. "Karhunen–Loeve expansions for the detrended Brownian motion," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1235-1241.
    2. Deheuvels, Paul, 2007. "A Karhunen-Loeve expansion for a mean-centered Brownian bridge," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1190-1200, July.
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    Cited by:

    1. Nazarov, Alexander & Petrova, Yulia, 2024. "L2-small ball asymptotics for some demeaned Gaussian processes," Statistics & Probability Letters, Elsevier, vol. 206(C).

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