%0 Journal Article
%T Some applications of duality for L¨¦vy processes in a half-line
%A Jean Bertoin
%A Mladen Savov
%J Mathematics
%D 2009
%I arXiv
%R 10.1112/blms/bdq084
%X The central result of this paper is an analytic duality relation for real-valued L\'evy processes killed upon exiting a half-line. By Nagasawa's theorem, this yields a remarkable time-reversal identity involving the L\'evy process conditioned to stay positive. As examples of applications, we construct a version of the L\'evy process indexed by the entire real line and started from $-\infty$ which enjoys a natural spatial-stationarity property, and point out that the latter leads to a natural Lamperti-type representation for self-similar Markov processes in $(0,\infty)$ started from the entrance point 0+.
%U http://arxiv.org/abs/0912.0131v1