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The rank of the present excursion

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  • Scheffer, Carel L.

Abstract

It is shown that for standard Brownian motion the present excursion from 0 has probability 0.80031 ... of establishing a record as far as its duration is concerned. This follows from a more general result concerning the rank of an excursion in the point process representation of a renewal process having interarrival times, the distribution of which varies regularly at infinity with exponent p [epsilon]] - 1,0[. Using Palm probabilities for Poisson processes one finds in fact the generating function of this rank explicitly.

Suggested Citation

  • Scheffer, Carel L., 1995. "The rank of the present excursion," Stochastic Processes and their Applications, Elsevier, vol. 55(1), pages 101-118, January.
    • Handle: RePEc:eee:spapps:v:55:y:1995:i:1:p:101-118
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    Cited by:

    1. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2017. "Record statistics of a strongly correlated time series: random walks and L\'evy flights," Papers 1702.00586, arXiv.org.
    2. J. Anderluh & J. Weide, 2009. "Double-sided Parisian option pricing," Finance and Stochastics, Springer, vol. 13(2), pages 205-238, April.

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    Keywords

    Excursions Current lifetime;

    Statistics

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