2019
2018
2017
2016
2015
2014
2013
2012
2011
2010
2009
2008
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
1977
1976
1975
1974
1973
1972
1971
1970


Archive

About   Editorial Board   Contacts   Template   Publication Ethics   Peer Review Process

Theory of Probability and Mathematical Statistics
(Teoriya Imovirnostei ta Matematychna Statystyka)



Stability estimates for transition probabilities of time-inhomogeneous Markov chains under the condition of the minorization on the whole space

V. Golomoziy

Download PDF

Abstract: In this paper we derive stability estimates for transition probabilities of two time-inhomo\-ge\-ne\-ous Markov chains with discrette time on the general state space.

Keywords:

Bibliography:
re obtained using two conditions: minorization on the whole space condition which is equivalent to the uniformal mixing, and proximity condition for transition
probabilities. Different types of proximity conditions are considered.
Bibliography: 1. W. Doeblin, Expose de la theorie des chaines simples constantes de Markov a un nomber fini d'estats, Mathematique de l'Union Interbalkanique, 2 (1938), 77-105.
2. N.V. Kartashov, Strong Stable Markov Chains, VSP, Utrecht, 1996.
3. P. Ney, A renement of the coupling method in renewal theory, Stochastic Processes Appl., 11 (1981), 11-26.
4. T. Lindvall, Lectures on the Coupling Method, John Wiley and Sons, New York, 1991.
5. T. Lindvall, On coupling for continuous time renewal processes, J. Appl. Probab., 19 (1982), 82-89.
6. H. Thorisson, The coupling of regenerative processes, Adv. Appl. Probab., 15 (1983), 531-561.
7. H. Thorisson, Coupling, Stationarity, and Regeneration, Springer, New York, 2000.
8. R. Douc, E. Moulines, J. S. Rosenthal, Quantitative bounds for geometric convergence rates of Markov chains, Annals of Applied Probability, 14 (2004), 1643-1664.
9. R. Douc, E. Mouliness, P. Solier, Subgeometric ergodicity of Markov chains, Dependence in Probability and Statistics, (2007), 55-64.
10. R. Douc, E. Moulines, P. Soulier, Computable convergence rates for sub-geometric ergodic Markov chains, Bernoulli, 13 (2007), no. 3, 831-848.
11. V. Golomoziy, Stability of inhomogeneous Markov chains, Vysnik Kyivskogo Universitety, 4 (2009), 10-15. (Ukrainian)
12. V. Golomoziy, A subgeometric estimate of the stability for time-homogeneous Markov chains, Theory of probability and mathematical statistics, 81 (2010), 35-50.
13. N. Kartashov, V. Golomoziy, Maximal coupling procedure and stability of discrete Markov chains. I, Theory of probability and mathematical statistics, 86 (2012), 81-92.
14. N. Kartashov, V. Golomoziy, Maximal coupling procedure and stability of discrete Markov chains. II, Theory of probability and mathematical statistics, 87 (2012), 58-70.
15. V. Golomoziy, N. Kartashov On coupling moment integrability for time-inhomogeneous Markov chains, Theory of probability and mathematical statistics, 89 (2014), 1-12.
16. N. Kartashov, V. Golomoziy, Maximal coupling and stability of discrete non-homogeneous Markov chains, Theory of probability and mathematical statistics, 91 (2015), 17-27.
17. V. Golomoziy, N. Kartashov, Y. Kartashov, Impact of the stress factor on the price of widow's pensions. Proofs, Theory of probability and mathematical statistics, 92 (2016), 17-22.
18. V. Kalashnikov, Estimation of duration of transition regime for complex stochastic systems, Trans. Seminar, VNIISI, Moscow (1980), 63-71.
19. D. Grieath, A maximal coupling for Markov chains, Z. Wahrsch. verw. Gebiete, 31 (1975), 95-106.
20. Y. Kartashov, V. Golomoziy, N. Kartashov, The impact of stress factor on the price of widow's pension, Modern Problems in Insurance Mathematics (D. Silverstrov and A. Martin-Lof, eds.), E. A. A. Series, Springer, 2014, 223-237.
21. D. Silvestrov, Synchronized regenerative processes and upper estimates for rate of convergence in ergodic theorems, Rep. Acad. Sci. Ukraine, Series A, 11 (1980), 22-25.
22. D. Silvestrov, Upper estimators in ergodic theorems for regenerative processes, Elektron. Inform. Kybernetik, 16, no. 8/9, (1980), 461-463.
23. D. Silvestrov, Method of a single probability space in ergodic theorems for regenerative processes, 1-3. Math. Operat. Statist., Ser. Optim. Part 1, 14 (1983), no. 2, 285299, Part 2: 16 (1984), no. 4, 216-231, Part 3: 16 (1984), no. 4, 232-244.
24. D. Silvestrov, Coupling for Markov renewal processes and the rate of convergence in ergodic theorems for processes with semi-Markov switchings. Acta Appl. Math., 34 (1994), 109-124.
25. J. W. Pitman, On coupling of Markov chains, Z. Wahrsch. verw. Gebiete, 35 (1979), 315-322.