Geodesic
Stochastic control of discrete Markov process parameter
Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 58-60.

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Consider a functioning of discrete Markov process in random environment. That is the process behavior is defined by some randomly varying parameter. Suppose that stationary distributions of the process under fixed meanings of the parameter are known. A problem is to choose rules of parameter ramdom variation so that the stationary distribution of obtained process equals to probability mixture of stationary distributions of this process under fixed parameter meanings. Traditional product theorem gives a respond to this question only if stationary distributions, which correspond to the fixed parameter meanings, coincide with each other. In this paper new and sufficiently simple condition on random parameter variation is introduced. This condition gives a solution of considered problem in general case. 
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G. Sh. Tsitsiashvili; M. A. Osipova. Stochastic control of discrete Markov process parameter. Dalʹnevostočnyj matematičeskij žurnal, Tome 3 (2002) no. 1, pp. 58-60. http://geodesic.mathdoc.fr/item/DVMG_2002_3_1_a5/

[1] F. P. Kelly, Reversibility and Stochastic Networks, John Wiley Sons, 1979 | MR | Zbl

[2] Y. Zhu, “Markovian Queueing Networks in Random Environment”, Operations Research Letters, 15 (1994), 11–17 | DOI | MR | Zbl

[3] D. Baum, G. Sh. Tsitsiashvili, “On Product Connection Theorems for Markov Chains”, Int. J. Pure Appl. Math., 1:2 (2002), 167–196 | MR | Zbl

[4] M. A. Osipova, G. Sh. Tsitsiashvili, N. V. Kolev, “Vychislenie statsionarnogo raspredeleniya v adaptivnykh setyakh massovogo obsluzhivaniya”, Dalnevost. matem. zhurn., 2:2 (2001), 99–105