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Boundary non-crossing probabilities for Slepian process

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  • Deng, Pingjin

Abstract

In this contribution we derive an explicit formula for the boundary non-crossing probability of Slepian processes associated with a continuous piecewise linear boundary function. Furthermore, we use this formula to develop an approximation result to the boundary non-crossing probability for general continuous boundaries.

Suggested Citation

  • Deng, Pingjin, 2017. "Boundary non-crossing probabilities for Slepian process," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 28-35.
    • Handle: RePEc:eee:stapro:v:122:y:2017:i:c:p:28-35
    DOI: 10.1016/j.spl.2016.10.026
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    References listed on IDEAS

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    1. Wolfgang Bischoff & Frank Miller & Enkelejd Hashorva & Jürg Hüsler, 2003. "Asymptotics of a Boundary Crossing Probability of a Brownian Bridge with General Trend," Methodology and Computing in Applied Probability, Springer, vol. 5(3), pages 271-287, September.
    2. Wolfgang Bischoff & Enkelejd Hashorva & Jürg Hüsler & Frank Miller, 2005. "Analysis of a change-point regression problem in quality control by partial sums processes and Kolmogorov type tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(1), pages 85-98, September.
    3. Bischoff, Wolfgang & Hashorva, Enkelejd & Hüsler, Jürg & Miller, Frank, 2004. "On the power of the Kolmogorov test to detect the trend of a Brownian bridge with applications to a change-point problem in regression models," Statistics & Probability Letters, Elsevier, vol. 66(2), pages 105-115, January.
    4. Bischoff, Wolfgang & Gegg, Andreas, 2016. "Boundary crossing probabilities for (q,d)-Slepian-processes," Statistics & Probability Letters, Elsevier, vol. 118(C), pages 139-144.
    5. Griselda Deelstra, 1994. "Remarks on Boundary crossing..," ULB Institutional Repository 2013/7576, ULB -- Universite Libre de Bruxelles.
    6. Wolfgang Bischoff & Enkelejd Hashorva & Jürg Hüsler & Frank Miller, 2003. "Exact asymptotics for Boundary crossings of the brownian bridge with trend with application to the Kolmogorov test," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(4), pages 849-864, December.
    7. Liu, Jin V. & Huang, Zongfu & Mao, Hongjun, 2014. "Karhunen–Loève expansion for additive Slepian processes," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 93-99.
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    Cited by:

    1. Pingjin Deng & Xiufang Li, 2017. "Barrier Options Pricing With Joint Distribution Of Gaussian Process And Its Maximum," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-18, September.

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