Curve crossing for the reflected Lévy process at zero and infinity. (English) Zbl 1190.60037

Savov, Mladen Svetoslavov

Electron. J. Probab. 13, 157-172 (2008).

Summary: Let \(R_t\) be a Levy process reflected in its maximum. We give necessary and sufficient conditions for finiteness of passage times above power law boundaries at infinity. Information as to when the expected passage time for \(R_t\) is finite, is given. We also discuss the almost sure finiteness of \(\limsup R_t/t^k\), for each \(k\geq0\).

MSC:

60G51	Processes with independent increments; Lévy processes
60F15	Strong limit theorems
60K05	Renewal theory
60G40	Stopping times; optimal stopping problems; gambling theory
60G44	Martingales with continuous parameter

Keywords:

reflected process; passage times; power law boundaries