Electronic Communications in Probability

Right inverses of Levy processes: the excursion measure in the general case

Mladen Savov and Matthias Winkel

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This article is about right inverses of Lévy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.

Article information

Electron. Commun. Probab., Volume 15 (2010), paper no. 51, 572-584.

Accepted: 12 December 2010
First available in Project Euclid: 6 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G51: Processes with independent increments; Lévy processes

Levy process right inverse subordinator fluctuation theory excursion

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Savov, Mladen; Winkel, Matthias. Right inverses of Levy processes: the excursion measure in the general case. Electron. Commun. Probab. 15 (2010), paper no. 51, 572--584. doi:10.1214/ECP.v15-1590. https://projecteuclid.org/euclid.ecp/1465243994

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