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The limit behavior of dual Markov branching processes. (English) Zbl 1137.60039

Summary: A dual Markov branching process (DMBP) is by definition a Siegmund’s predual of some Markov branching process (MBP). Such a process does exist and is uniquely determined by the so-called dual-branching property. Its \(q\)-matrix \(Q\) is derived and proved to be regular and monotone. Several equivalent definitions for a DMBP are given. The criteria for transience, positive recurrence, strong ergodicity, and the Feller property are established. The invariant distributions are given by a clear formulation with a geometric limit law.

MSC:

60J27 Continuous-time Markov processes on discrete state spaces
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
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