Conditioning to avoid bounded sets for a one-dimensional Lévy processes

Abstract

For several classes of bounded sets $A$, the limit of a one-dimensional Lévy process conditioned to avoid $A$ up to a parametrized random time which tends to infinity. For $A$ we take the set of finite points with several clocks and a bounded $F_{\ddot{I}}ƒ$-set with exponential clock. We also take an integer lattice with exponential clock.