Computable convergence rates for sub-geometric ergodic Markov chains

Bernoulli

Volumn 13, Issue 3, 2007, Pages 831-848

  Douc, Randal ^a   Moulines, Eric ^b   Soulier, Philippe ^c  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b TELECOM PARISTECH   (France)

^c UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

Author keywords

Markov chains; Rates of convergence; Stochastic monotonicity

Indexed keywords

EID: 47249094432     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ5162     Document Type: Article

References (27)

1. Baxendale, P.H. (2005). Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15 700-738.
2. Dai, J.G. and Meyn, S.P. (1995). Stability and convergence of moments for multiclass queueing networks via fluid limit models. IEEE Trans. Automat. Control 40 1889-1904.
3. Douc, R., Fort, G., Moulines, E. and Soulier, P. (2004a). Practical drift conditions for subgeometric rates of convergence. Ann. Appl. Probab. 14 1353-1377.
4. Douc, R., Moulines, E. and Rosenthal, J. (2004b). Quantitative bounds for geometric convergence rates of Markov chains. Ann. Appl. Probab. 14 1643-1665.
5. Fort, G. (2001). Contrôle explicite d'ergodicité de chaines de Markov: applications à l'analyse de convergence de l'algorithme Monte-Carlo EM. Ph.D. thesis, Université de Paris VI. INIST Number
6. Fort, G. and Moulines, E. (2000). V-subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Probab. Lett. 49 401-410.
7. Fort, G. and Moulines, E. (2003). Polynomial ergodicity of Markov transition kernels. Stochastic Process. Appl. 103 57-99.
8. Gulinsky, O.V. and Veretennikov, A.Y. (1993). Large Deviations for Discrete-Time Processes with Averaging. Utrecht: VSP.
9. Jarner, S.F. and Roberts, G.O. (2002). Polynomial convergence rates of Markov chains. Ann. Appl. Probab. 12 224-247.
10. Klokov, S.A. and Veretennikov, A.Y. (2004). Sub-exponential mixing rate for a class of Markov chains. Math. Commun. 9 9-26.
11. Lindvall, T. (1979). On coupling of discrete renewal sequences. Z. Wahrsch. Verw. Gebiete 48 57-70.
12. Lindvall, T. (1992). Lectures on the Coupling Method. New York: Wiley.
13. Lund, R.B., Meyn, S.P. and Tweedie, R. (1996). Computable exponential convergence rates for stochastically ordered Markov processes. Ann. Appl. Probab. 6 218-237.
14. Lund, R.B. and Tweedie, R.L. (1996). Geometric convergence rates for stochastically ordered Markov chains. Math. Oper. Res. 21 182-194.
15. Meyn, S.P. and Tweedie, R.L. (1993). Markov Chains and Stochastic Stability. London: Springer.
16. Meyn, S.P. and Tweedie, R.L. (1994). Computable bounds for convergence rates of Markov chains. Ann. Appl. Probab. 4 991-1011.
17. Nummelin, E. and Tuominen, P. (1983). The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory. Stochastic Process. Appl. 15 295-311.
18. Roberts, G.O. and Rosenthal, J.S. (2004). General state space Markov chains and MCMC algorithms. Probab. Surv. 1 20-71.
19. Roberts, G.O. and Tweedie, R.L. (1999). Bounds on regeneration times and convergence rates for Markov chains. Stochastic Process. Appl. 80 211-229.
20. Roberts, G.O. and Tweedie, R.L. (2000). Rates of convergence of stochastically monotone and continuous time Markov models. J. Appl. Probab. 37 359-373.
21. Rosenthal, J.S. (1995). Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90 558-566.
22. Roughan, M., Veitch, D. and Rumsewicz, M. (1998). Computing queue-length distributions for power-law queues. In Proceedings IEEE INFOCOM '98 1 356-363.
23. Scott, D.J. and Tweedie, R.L. (1996). Explicit rates of convergence of stochastically ordered Markov chains. Athens Conference on Applied Probability and Time Series Analysis 1. Applied Probability in Honor of J. M. Gani. Lecture Notes in Statist. 114 176-191. New York: Springer.
24. Thorisson, H. (2000). Coupling, Stationarity and Regeneration. New York: Springer.
25. Tuominen, P. and Tweedie, R. (1994). Subgeometric rates of convergence of f-ergodic Markov chains. Adv. in Appl. Probab. 26 775-798.
26. Veretennikov, A. (1997). On polynomial mixing bounds for stochastic differential equations. Stochastic Process. Appl. 70 115-127.
27. Veretennikov, A. (2000). On polynomial mixing and the rate of convergence for stochastic differential and difference equations. Theory Probab. Appl. 44 361-374.