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The Joint Distribution of Running Maximum of a Slepian Process

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  • Pingjin Deng

    (Nankai University
    University of Lausanne)

Abstract

Consider the Slepian process S defined by S(t) = B(t + 1) − B(t),t ∈ [0, 1] with B(t), t ∈ ℝ a standard Brownian motion. In this contribution we analyze the properties between the maximum m s = max 0 ≤ u ≤ s S ( u ) $m_{s}=\max \limits _{0\leq u\leq s}S(u)$ and the maximum m t = max 0 ≤ u ≤ t S ( u ) $m_{t}=\max \limits _{0\leq u\leq t}S(u)$ for 0 ≤ s

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:4:d:10.1007_s11009-017-9594-z
    DOI: 10.1007/s11009-017-9594-z
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Pingjin Deng, 2016. "The boundary non-Crossing probabilities for Slepian process," Papers 1608.01133, arXiv.org.
    3. Abundo, Mario, 2016. "On the excursions of drifted Brownian motion and the successive passage times of Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 176-182.
    4. Dieker, A.B., 2005. "Extremes of Gaussian processes over an infinite horizon," Stochastic Processes and their Applications, Elsevier, vol. 115(2), pages 207-248, February.
    5. 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.
    6. Dȩbicki, Krzysztof & Hashorva, Enkelejd & Ji, Lanpeng & Tabiś, Kamil, 2015. "Extremes of vector-valued Gaussian processes: Exact asymptotics," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4039-4065.
    7. Popivoda, Goran & Stamatović, Siniša, 2016. "Extremes of Gaussian fields with a smooth random variance," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 185-190.
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