Stationary measures and the continuous-state branching process conditioned on extinction
Stationary measures and the continuous-state branching process conditioned on extinction
Abstract We consider continuous-state branching processes (CB processes) which become extinct almost surely. First, we tackle the problem of describing the stationary measures on $(0,+\infty)$ for such CB processes. We give a representation of the stationary measure in terms of scale functions of related Lévy processes. Then we prove that …