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Issue 3
Sep.  2016
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ZHU Yi-Xia. Quasi-stationary distributions for absorbing stochastically monotone Markov chains[J]. Journal of East China Normal University (Natural Sciences), 2016, (3): 48-59. doi: 2016.03.006
Citation: ZHU Yi-Xia. Quasi-stationary distributions for absorbing stochastically monotone Markov chains[J]. Journal of East China Normal University (Natural Sciences), 2016, (3): 48-59. doi: 2016.03.006

Quasi-stationary distributions for absorbing stochastically monotone Markov chains

doi: 2016.03.006
  • Received Date: 2015-05-12
  • Publish Date: 2016-05-25
  • In this paper, we prove some limit theorems for absorbing stochastically monotone Markov chain during its lifetime. The emphases are on the stationary conditional, doubly limiting conditional and limiting conditional mean ratio quasi-stationary distributions. We study the uniqueness and domain of attraction of three types of quasi-stationary distributions for stochastically monotone Markov chains. A sufficient condition for the uniqueness of the three types of quasi-stationary distributions is given in our main results and under this condition, the unique quasi-stationary distribution attracts all initial distributions. We apply the main results to birth and death processes.
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  • [1]POLLETT P K. Quasi stationary distributions: A bibliography R/OL].(2015-03-13)2015-03-30].http://www.maths.uq.edu.au/\simpkp/papers/qsds/qsds.pdf.
    [2]DARROCH J N, SEBETA E. On quasi-stationary distributions in absorbing discrete-time finite Markov chains J]. Journal of Applied Probability, 1965(2): 88-100.
    [3]DARROCH J N, SEBETA E. On quasi-stationary distributions in absorbing continuous-time finite Markov chains J]. Journal of Applied Probability, 1967(4): 192-196.
    [4]SENETA E, VERE-JONES D. On quasi-stationary distributions in discrete-time Markov chains with a denumerable infinity of states[J]. Journal of Applied Probability, 1966(3): 403-434.
    [5]FLASPOHLER D C. Quasi-stationary distributions for absorbing continuous-time denumerable Markov chains J]. Annals of the Institute of Statistical Mathematics, 1974, 26(1): 351-356.
    [6]PAKES A G. Quasi-stationary laws for Markov processes: examples of an always proximate absorbing state J]. Advances in Applied Probability, 1995, 27: 120-145.
    [7]KINGMAN J F C. The exponential deacy of Markov transition probabilities J]. Proceedings of the London Mathematical Society,1963, 13: 337-358.
    [8]ANDERSON W J. Continuous-Time Markov Chains: An Applications-Oriented Approach M]. New York: Springer, 1991.
    [9]VAN DOORN E A. Quasi-stationary distributions and convergence to quasi-stationarity of birth-death processes J]. Advances in Applied Probability, 1991, 23: 683--700.
    [10]ZHANG H J, ZHU Y X. Domain of attraction of the quasistationary distribution for birth and death processes J]. Journal of Applied Probability, 2013, 50: 114-126.
    [11]CHEN A Y, ZHANG H J. Existence, uniqueness, and constructions for stochastically monotone Q-processes J]. Southeast Asian Bulletin of Mathematics, 1999, 23: 559-583.
    [12]JACKA S D, ROBERS G O. Weak convergrnce of conditioned processes on a countable state space J]. Journal of Applied Probability, 1995,32: 902-916.
    [13]VERE-JONES D. Ergodic Properties of non-negative matrices I J].Pacific Journal of Mathematics, 1967, 22(2): 361-385.
    [14]KARLIN S, MCGREGOR J L. The classification of birth and death processes J]. Transactions of the American Mathematical Society,1957, 86: 366-400.
    [15]KARLIN S, TAYLOR H M.  A First Course in Stochastic Processes M].2nd ed. New York: Academic press, 1975.
     
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