A NOTE ON FIRST PASSAGE PROBABILITIES OF A LÉVY PROCESS
REFLECTED AT A GENERAL BARRIER
Zbigniew Palmowski
Przemysław Świątek
Abstract: In this paper we analyze a Lévy process reflected at a general (possibly random)
barrier. For this process we prove the Central Limit Theorem for the first passage time. We
also give the finite-time first passage probability asymptotics.
2010 AMS Mathematics Subject Classification: Primary: 60G51, 60G50; Secondary:
60K25.
Keywords and phrases: Reflected Lévy process, Central Limit Theorem, asymptotics,
first passage probability.