Right inverses of Lévy processes

Ron Doney; Mladen Savov

doi:10.1214/09-AOP515

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Home > Journals > Ann. Probab. > Volume 38 > Issue 4 > Article

July 2010 Right inverses of Lévy processes

Ron Doney, Mladen Savov

Ann. Probab. 38(4): 1390-1400 (July 2010). DOI: 10.1214/09-AOP515

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Abstract

We call a right-continuous increasing process K_x a partial right inverse (PRI) of a given Lévy process X if X_{K_x} = x for at least all x in some random interval [0, ζ) of positive length. In this paper, we give a necessary and sufficient condition for the existence of a PRI in terms of the Lévy triplet.