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The joint distributions of running maximum of a Slepian processes

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  • Pingjin Deng

Abstract

Consider the Slepian process $S$ defined by $ S(t)=B(t+1)-B(t),t\in [0,1]$ with $B(t),t\in \R$ a standard Brownian motion.In this contribution we analyze the joint distribution between the maximum $m_{s}=\max_{0\leq u\leq s}S(u)$ certain and the maximum $M_t=\max_{0\leq u\leq t}S(u)$ for $0

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  • Pingjin Deng, 2016. "The joint distributions of running maximum of a Slepian processes," Papers 1609.04529, arXiv.org.
    • Handle: RePEc:arx:papers:1609.04529
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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. 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.
    3. 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.
    4. Pingjin Deng, 2016. "The boundary non-Crossing probabilities for Slepian process," Papers 1608.01133, arXiv.org.
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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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