Abstract
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.
Original language | English |
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Pages (from-to) | 176-189 |
Journal | Journal of Applied Probability |
Volume | 45 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2008 |