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October, 1980 Markov Chains in Random Environments: The Case of Markovian Environments
Robert Cogburn
Ann. Probab. 8(5): 908-916 (October, 1980). DOI: 10.1214/aop/1176994620


A formulation of a Markov chain in a random environment is given, generalizing special cases such as branching processes, queues, birth and death chains and random walks in random environments. It is assumed that the environmental process is Markovian, each environment corresponding to a particular law of evolution on a countable state space $\mathscr{X}$. It is then shown that there is a natural three way classification of states of $\mathscr{X}$. One of the three types of states is irregular in nature, and conditions are found under which no such states exist.


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Robert Cogburn. "Markov Chains in Random Environments: The Case of Markovian Environments." Ann. Probab. 8 (5) 908 - 916, October, 1980.


Published: October, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0444.60053
MathSciNet: MR586775
Digital Object Identifier: 10.1214/aop/1176994620

Primary: 60J05
Secondary: 60J99

Keywords: bichain , classification of states , improperly essential , inessential , Markov chains in random environments , Markovian environments , proper bichain , properly essential

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • October, 1980
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