Open Access
2010 Right inverses of Levy processes: the excursion measure in the general case
Mladen Savov, Matthias Winkel
Author Affiliations +
Electron. Commun. Probab. 15: 572-584 (2010). DOI: 10.1214/ECP.v15-1590


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.


Download Citation

Mladen Savov. Matthias Winkel. "Right inverses of Levy processes: the excursion measure in the general case." Electron. Commun. Probab. 15 572 - 584, 2010.


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

zbMATH: 1226.60071
MathSciNet: MR2746335
Digital Object Identifier: 10.1214/ECP.v15-1590

Primary: 60G51

Keywords: excursion , fluctuation theory , Levy process , right inverse , subordinator

Back to Top