Right inverses of Lévy processes. (English) Zbl 1196.60084

Summary: 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 \([0, \zeta \)) 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.


60G51 Processes with independent increments; Lévy processes
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