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The boundary non-Crossing probabilities for Slepian process

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  • Pingjin Deng

Abstract

In this contribution we derive an explicit formula for the boundary non-crossing probabilities for Slepian processes associated with the piecewise linear boundary function. This formula is used to develop an approximation formula to the boundary non-crossing probabilities for general continuous boundaries. The formulas we developed are easy to implement in calculation the boundary non-crossing probabilities.

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  • Pingjin Deng, 2016. "The boundary non-Crossing probabilities for Slepian process," Papers 1608.01133, arXiv.org.
    • Handle: RePEc:arx:papers:1608.01133
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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. Griselda Deelstra, 1994. "Remarks on Boundary crossing..," ULB Institutional Repository 2013/7576, ULB -- Universite Libre de Bruxelles.
    4. 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.
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    Cited by:

    1. Pingjin Deng, 2016. "The joint distributions of running maximum of a Slepian processes," Papers 1609.04529, arXiv.org.
    2. Pingjin Deng, 2018. "The Joint Distribution of Running Maximum of a Slepian Process," Methodology and Computing in Applied Probability, Springer, vol. 20(4), pages 1123-1135, December.

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