Creeping of Lévy processes through curves

A Lévy process is said to creep through a curve if, at its first passage time across this curve, the reaches it with positive probability. We study property for bivariate subordinators. Given graph {(t,f(t)):t≥0} of any continuous, non increasing function f such that f(0)>0, we give an expression probability subordinator (Y,Z) issued from 0 creeps in terms renewal and drifts components Y Z. apply result creeping real where also past supremum. This involves density upward ladder as well drift coefficients. investigate case processes conditioned stay their last below function. Then provide some examples application fixed levels by stable Ornstein-Uhlenbeck processes. raise couple open questions along text.