1980
DOI: 10.1214/aop/1176994620
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Markov Chains in Random Environments: The Case of Markovian Environments

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Cited by 74 publications
(27 citation statements)
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“…Optimization of service rate for the case when arrival rate is a Markov process is studied in [26]. See also, a birthdeath process in random environment [13] and a Markov chain in Markov environment, studied in [12,16,33]. A particular case of a Markov-modulated setting is when the service dynamics is subject to interruptions.…”
Section: 1mentioning
confidence: 99%
“…Optimization of service rate for the case when arrival rate is a Markov process is studied in [26]. See also, a birthdeath process in random environment [13] and a Markov chain in Markov environment, studied in [12,16,33]. A particular case of a Markov-modulated setting is when the service dynamics is subject to interruptions.…”
Section: 1mentioning
confidence: 99%
“…Repeating this step n times, we obtain Eq. (6). Applying (M1), for bounded measurable functions g and h from 1 ( ) t + Θ X andX to R respectively, we have…”
Section: The Equivalence Theoremsmentioning
confidence: 99%
“…Kalikow [2] , Sinai [3] , and Sznaitman [4] studied deeply the model. At the same time, Nawrotzki [5] , and Cogburn [6][7][8] , also established a general model of Markov chains in random environments, and Orey [9] reviewed the works on this field and also gave some new results and open problems in a special invited paper. Please notice that the model of Solomon is space random environments, i.e.…”
mentioning
confidence: 99%
“…For details, see the Refs. [1][2][3][4][5][6][7][8][9][10], for Markov chains in random environment, the ergodic of recurrent, positive recurrent and the period of a state of Markov chains in random environment had been introduced. Li given the condition of m-irreducible in Ref.…”
Section: Introductionmentioning
confidence: 99%