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Approximating Shepp’s constants for the Slepian process

Author

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  • Noonan, Jack
  • Zhigljavsky, Anatoly

Abstract

Slepian process S(t) is a stationary Gaussian process with zero mean and covariance ES(t)S(t′)=max{0,1−|t−t′|}. For any T≥0 and real h, define FT(h)=Prmaxt∈[0,T]S(t)

Suggested Citation

  • Noonan, Jack & Zhigljavsky, Anatoly, 2019. "Approximating Shepp’s constants for the Slepian process," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 21-31.
    • Handle: RePEc:eee:stapro:v:153:y:2019:i:c:p:21-31
    DOI: 10.1016/j.spl.2019.05.001
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    References listed on IDEAS

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    1. Jack Noonan & Anatoly Zhigljavsky, 2018. "Approximations of the boundary crossing probabilities for the maximum of moving weighted sums," Statistical Papers, Springer, vol. 59(4), pages 1325-1337, December.
    2. G. Molchan, 2012. "Survival Exponents for Some Gaussian Processes," International Journal of Stochastic Analysis, Hindawi, vol. 2012, pages 1-20, November.
    3. Jinn‐Tyan Lin, 1989. "Approximating the Normal Tail Probability and its Inverse for Use on a Pocket Calculator," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 38(1), pages 69-70, March.
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