On suprema of Lévy processes and application in risk theory
Renming Song, Zoran Vondraček (2008)
Annales de l'I.H.P. Probabilités et statistiques
Similarity:
Let =− where is a general one-dimensional Lévy process and an independent subordinator. Consider the times when a new supremum of is reached by a jump of the subordinator . We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and drifts to −∞, we decompose the absolute supremum of at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.