Occupation time distributions for Lévy bridges and excursions

P. J. Fitzsimmons and R. K. Getoor

Stochastic Processes and their Applications, 1995, vol. 58, issue 1, 73-89

Abstract: Let X be a one-dimensional Lévy process. It is shown that under the bridge law for X starting from 0 and ending at 0 at time t, the amount of time X spends positive has a uniform distribution on [0, t]. When 0 is a regular point, this uniform distribution result leads to an explicit expression for the Laplace transform of the joint distribution of the pair (R, AR), where R is the length of an excursion of X from 0, and AR is the total time X spends positive during the excursion. More concrete expressions are obtained for stable processes by specialization. In particular, a formula determining the distribution of AR/R is given in the stable case.

Keywords: Lévy; process; Lévy; bridge; Excursion; Occupation; time; Uniform; distribution (search for similar items in EconPapers)
Date: 1995
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Citations: View citations in EconPapers (5)

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