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Discrete and continuous expectation formulae for level-crossings, upcrossings and excursions of ellipsoidal processes

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  • Tanaka, Minoru
  • Shimizu, Kunio
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    Abstract

    The paper provides the expected level-crossing count, the expected level-crossing rate, the expected number of upcrossings and the expected length of excursions above a fixed level in a strictly stationary ellipsoidal process whose finite dimensional distributions are scale mixtures of normal distributions.

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    File URL: http://www.sciencedirect.com/science/article/B6V1D-42VM8V5-1/2/99c00d2a40caa2168b0a2b16de0149a0
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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 52 (2001)
    Issue (Month): 3 (April)
    Pages: 225-232

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    Handle: RePEc:eee:stapro:v:52:y:2001:i:3:p:225-232

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    Related research

    Keywords: Arcsine formula Gaussian process Level-crossing Pearson Type VII density Rice's formula Scale mixtures of normals Upcrossing;

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    Cited by:
    1. Alexeev, Vitali & Maynard, Alex, 2012. "Localized level crossing random walk test robust to the presence of structural breaks," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3322-3344.
    2. Shimizu, Kunio & Tanaka, Minoru, 2003. "Expected number of level-crossings for a strictly stationary ellipsoidal process," Statistics & Probability Letters, Elsevier, vol. 64(3), pages 305-310, September.

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