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Perturbations of countable Markov chains and processes. (English) Zbl 0452.60075


MSC:

60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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References:

[1] Chung, K. L. (1967).Markov Chains with Stationary Transition Probabilities, (2nd Ed.), Springer-Verlag, Berlin. · Zbl 0146.38401
[2] Çinlar, E. (1975).Introduction to Stochastic Processes, Prentice-Hall, New Jersey. · Zbl 0341.60019
[3] Jensen, A. and Kendall, D. G. (1971). Denumerable Markov processes with bounded generators: a routine for calculatingpij(∞),J. Appl. Prob.,8, 423-427. · Zbl 0231.60047 · doi:10.2307/3211914
[4] Schweitzer, P. J. (1968). Perturbation theory and finite Markov chains,J. Appl. Prob.,5, 401-413. · Zbl 0196.19803 · doi:10.2307/3212261
[5] Seneta, E. (1967). Finite approximations to non-negative matrices,Proc. Camb. Phil. Soc.,63, 983-992. · Zbl 0178.20602 · doi:10.1017/S0305004100042006
[6] Seneta, E. (1968). Finite approximations to non-negative matrices II: refinements and applications,Proc. Camb. Phil. Soc.,64, 465-470. · Zbl 0197.02802 · doi:10.1017/S0305004100043061
[7] Takahashi, Y. (1973). On the effects of small deviations in the transition matrix of a finite Markov chain,J. Operat. Res. Soc. Japan,16, 104-129. · Zbl 0271.60075
[8] Tweedie, R. L. (1973). The calculation of limit probabilities for denumerable Markov processes from infinitesimal properties,J. Appl. Prob.,10, 84-99. · Zbl 0258.60051 · doi:10.2307/3212497
[9] Tweedie, R. L. (1975). The robustness of positive recurrence and recurrence of Markov chains under perturbations of the transition probabilities.J. Appl. Prob.,12, 744-752. · Zbl 0324.60054 · doi:10.2307/3212725
[10] Tweedie, R. L. (1976). Criteria for classifying general Markov chains,Adv. Appl. Prob.,8, 737-771. · Zbl 0361.60014 · doi:10.2307/1425932
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