A note on first passage probabilities of a L\'evy process reflected at a   general barrier
  In this paper we analyze a L\'evy process reflected at a general (possibly random) barrier. For this process we prove Central Limit Theorem for the first passage time. We also give the finite-time first passage probability asymptotics. 
Zbigniew Palmowski and Przemys{\l}aw \'Swi\k{a}tek
math.PR