%0 Journal Article
%T On the Coupling Property of L¨¦vy Processes
%A Ren¨¦ L. Schilling
%A Jian Wang
%J Mathematics
%D 2010
%I arXiv
%R 10.1214/10-AIHP400
%X We give necessary and sufficient conditions guaranteeing that the coupling for L\'evy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall-Rogers on couplings of random walks. In particular, we obtain that a L\'{e}vy process admits a successful coupling, if it is a strong Feller process or if the L\'evy (jump) measure has an absolutely continuous component.
%U http://arxiv.org/abs/1006.5288v2