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On the excursions of drifted Brownian motion and the successive passage times of Brownian motion

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  • Abundo, Mario

Abstract

By using the law of the excursions of Brownian motion with drift, we find the distribution of the nth passage time of Brownian motion through a straight line S(t)=a+bt. In the special case when b=0, we extend the result to a space–time transformation of Brownian motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:457:y:2016:i:c:p:176-182
    DOI: 10.1016/j.physa.2016.03.052
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    References listed on IDEAS

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    1. Abundo, Mario, 2012. "An inverse first-passage problem for one-dimensional diffusions with random starting point," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 7-14.
    2. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
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    Cited by:

    1. 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.
    2. Pingjin Deng, 2016. "The joint distributions of running maximum of a Slepian processes," Papers 1609.04529, arXiv.org.

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