– Let X be a real Lévy process and let X↑ be the process conditioned to stay positive. We assume that 0 is regular for (−∞,0) and (0,+∞) with respect to X. Using elementary excursion theory arguments, we provide a simple probabilistic description of the reversed paths of X and X↑ at their first hitting time of (x,+∞) and last passage time of (−∞, x], on a fixed time interval [0, t], for a posit...
