@article{ECP1590,
author = {Mladen Savov and Matthias Winkel},
title = {Right inverses of Levy processes: the excursion measure in the general case},
journal = {Electron. Commun. Probab.},
fjournal = {Electronic Communications in Probability},
volume = {15},
year = {2010},
keywords = {Levy process, right inverse, subordinator, fluctuation theory, excursion},
abstract = {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.},
pages = {no. 51, 572-584},
issn = {1083-589X},
doi = {10.1214/ECP.v15-1590},
url = {http://ecp.ejpecp.org/article/view/1590}}