Convergence of Invariant Measures of Truncation Approximations to Markov Processes

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References

[1] W. Anderson, “Continuous-Time Markov Chains: An Applications-Oriented Approach,” Springer Series in Statistics, Springer-Verlag, New York, 1991.

[2] E. Seneta, “Finite Approximations to Infinite Nonnegative Matrices I,” Proceedings of the Cambridge Philosophical Society, Vol. 63, No. 4, 1967, pp. 983-992.
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[3] E. Seneta, “Finite Approximations to Infinite Nonnega tive Matrices II: Refinements and Applications,” Proceedings of the Cambridge Philosophical Society, Vol. 64, No. 2, 1968, pp. 465-470.
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[4] E. Seneta, “Computing the Stationary Distribution for Infinite Markov Chains,” Linear Algebra and Its Applications, Vol. 34, 1980, pp. 259-267.
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[5] D. Gibson and E. Seneta, “Monotone Infinite Stochastic Matrices and Their Augmented Truncations,” Stochastic Processes and Their Applications, Vol. 24, No. 2, 1987, pp. 287-292. doi:10.1016/0304-4149(87)90019-6

[6] D. Gibson and E. Seneta, “Augmented Truncations of Infinite Stochastic Matrices,” Journal of Applied Probability, Vol. 24, No. 3, 1987, pp. 600-608.
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[7] R. Tweedie, “Truncation Approximations of Invariant Measures for Markov Chains,” Journal of Applied Probability, Vol. 35, No. 3, 1998, pp. 517-536.
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[8] R. Tweedie, “Truncation Procedures for Nonnegative Matrices,” Journal of Applied Probability, Vol. 8, No. 2, 1971, pp. 311-320. doi:10.2307/3211901

[9] R. Tweedie, “The Calculation of Limit Probabilities for Denumerable Markov Processes from Infinitesimal Properties,” Journal of Applied Probability, Vol. 10, No. 1, 1973, pp. 84-99. doi:10.2307/3212497

[10] J. Kingman, “The Exponential Decay of Markov Transition Probabilities,” Proceedings of the London Mathematical Society, Vol. 13, No. 1, 1963, pp. 337-358.
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[11] D. Down, S. Meyn and R. Tweedie, “Exponential and Uniform Ergodicity of Markov Processes,” Annals of Probability, Vol. 23, No. 4, 1995, pp. 1671-1691.
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[12] R. Tweedie, “Criteria for Ergodicity, Exponential Ergodicity and Strong Ergodicity of Markov Processes,” Journal of Applied Probability, Vol. 18, No. 1, 1981, pp. 122-130. doi:10.2307/3213172

[13] S. Meyn and R. Tweedie, “Markov Chains and Stochastic Stability,” Springer-Verlag, London, 1993.
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[14] S. Meyn and R. Tweedie, “Computable Bounds for Convergence Rates of Markov Chains,” Annals of Applied Probability, Vol. 4, No. 4, 1994, pp. 981-1011.
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[15] B. Kirstein, “Monotonicity and Comparability of Time-Homogeneous Markov Processes with Discrete State Space,” Statistics, Vol. 7, No. 1, 1976, pp. 151-168.

[16] A. Hart, “Quasistationary Distributions for Continuous-Time Markov Chains,” Ph.D. thesis, University of Queensland, Brisbane, 1997.

[17] L. Breyer and A. Hart, “Approximations of Quasistationary Distributions for Markov Chains,” Mathematical and Computer Modelling, Vol. 31, No. 10-12, 2000, pp. 69-79.
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[18] M. Kijima and E. Seneta, “Some Results for Quasistationary Distributions of Birth-Death Processes,” Journal of Applied Probability, Vol. 28, No. 3, 1991, pp. 503-511.
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