The limit behavior of dual Markov Branching Processes

Y. Li; Anthony Pakes; J. Li; A. Gu

doi:10.1239/jap/1208358960

The limit behavior of dual Markov Branching Processes

Y. Li, Anthony Pakes, J. Li, A. Gu

UWA Business School

Research output: Contribution to journal › Article

3 Citations (Scopus)

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
Pages (from-to)	176-189
Journal	Journal of Applied Probability
Volume	45
Issue number	1
DOIs	https://doi.org/10.1239/jap/1208358960
Publication status	Published - 2008

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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.",

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AU - Gu, A.

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AB - 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.

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DO - 10.1239/jap/1208358960

M3 - Article

VL - 45

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EP - 189

JO - Journal of Applied Probability

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