The Boundedness of Branching Markov Processes

Abstract

This chapter continues [5]–[7], and its main concepts originally arose from problems in queueing network theory. In the course of later development, the relations with the theory of branching processes were discovered. We are very glad to note that the subject of this chapter is closely related to the problems which were and are the focus of attention of Professor E. B. Dynkin; see [1] and references therein. One author (F.I.K) was a student of Evgenii Borisovich; the others had opportunities to attend his lecture courses and seminars which always had an enormous impact on listeners and participants (not to mention the experience of being examined by him, remembered by everyone for life). We hope that these results will develop further in the direction of Professor Dynkin’s interest.