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The Distribution of the Sojourn Time for the Brownian Excursion

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  • Lajos Taka´cs

    (Case Western Reserve University)

Abstract

The solutions of various problems in the theories of queuing processes, branching processes, random graphs and others require the determination of the distribution of the sojourn time (occupation time) for the Brownian excursion. However, no standard method is available to solve this problem. In this paper we approximate the Brownian excursion by a suitably chosen random walk process and determine the moments of the sojourn time explicitly. By using a limiting approach, we obtain the corresponding moments for the Brownian excursion. The moments uniquely determine the distribution, enabling us to derive an explicit formula.

Suggested Citation

  • Lajos Taka´cs, 1999. "The Distribution of the Sojourn Time for the Brownian Excursion," Methodology and Computing in Applied Probability, Springer, vol. 1(1), pages 7-28, July.
    • Handle: RePEc:spr:metcap:v:1:y:1999:i:1:d:10.1023_a:1010060107265
    DOI: 10.1023/A:1010060107265
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    References listed on IDEAS

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    1. J. W. Cohen & G. Hooghiemstra, 1981. "Brownian Excursion, the M / M /1 Queue and Their Occupation Times," Mathematics of Operations Research, INFORMS, vol. 6(4), pages 608-629, November.
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