Cutting Markovian trees
Paavo Salminen · Annales Academiae Scientiarum Fennicae Series A I Mathematica · 1992
In this paper a path transformation of a branching Markov process is studied in which, roughly speaking, all finite branches are erased with unit speed from the tip of the branch for a given time g, 0 < g < oo.To have a more applicable touch we, in fact, transform killed branching processes.Killing is done at a terminal line.This notion is introduced as a generalization of the notion of terminal time.It is proved that the transformed process is again a branching Markov process and its law is characterized.This may be viewed as a generalization of a classical result of Harris [5], and a more recent tesult of Neveu [9].