Starting Markov processes from boundary points of the state space has a long history, dating back all the way to William Feller. In the present article we study different ways to start time-changed Lévy processes from infinity, a question that has attracted a lot of interest in the past decade for instance in the study of self-similar Markov processes or branching processes with state-dependent immigration.
Our main results give sharp conditions on the Lévy process and the time-change function to allow entrance or regular boundary.
Joint work with Leif Döring (Mannheim) and Samuel Baguley (Postdam).
