Polynomial ergodicity of Markov transition kernels

Stochastic Processes and their Applications

Volumn 103, Issue 1, 2003, Pages 57-99

  Fort, G ^a   Moulines, E ^b  

^a IMAG Institute   (France)

^b INSTITUT TELECOM   (France)

Author keywords

Computational methods in Markov chain; Markov chains with discrete parameters; Mixing; Polynomial convergence

Indexed keywords

EID: 0037210788     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(02)00182-5     Document Type: Article

References (27)

1. AngoNze, P., 1994. Critères d'ergodicitŕe de modèles markoviens. Estimation non-paramétrique sous des hypothèses de dépendance. Ph.D. Thesis, Univ. Paris IX- Dauphine, Paris.
2. AngoNze, P., 2000. Geometric and subgeometric rates for Markovian processes: a robust approach. Preprint-Université de Lille III.
3. Diaconis, P., Freedman, D., 1999. Iterated random functions. SIAM Rev. 41 (1), 45-76.
4. n. C.R. Acad. Sci. Paris Sér. A-B 291 (1), 61-63.
5. Dynkin, E.B., 1963. Théorie des processus markoviens. Dunod, Paris.
6. Fort, G., 2001. Contrôle explicite d'ergodicité de chaîne de Markov: applications à l'analyse de convergence de l'algorithme Monte-Carlo EM. Ph.D. Thesis, Université Pierre et Marie Curie, Paris.
7. Fort, G., Moulines, E., 2000. V-subgeometric ergodicity for a Hastings-Metropolis algorithm. Statist. Probab. Lett. 49 (4), 401-410.
8. Jarner, S.F., Hansen, E., 2000. Geometric ergodicity of Metropolis algorithms. Stochastic Processes Appl. 85 (2), 341-361.
9. Jarner, S., Roberts, G.O., 2002. Polynomial convergence rates of Markov Chains. Ann. Appl. Probab. 12 (1), 224-247.
10. Kalashnikov, V.V., 1994. Regeneration and general Markov Chains. J. Appl. Math. Stochastic Anal. 7 (3), 357-371.
11. Klüppelberg, C., 1988. Subexponential distributions and integrated tails. J. Appl. Probab. 25 (1), 132-141.
12. Mengersen, K.L., Tweedie, R.L., 1996. Rates of convergence of the Hastings and Metropolis algorithms. Ann. Statist. 24 (1), 101-121.
13. Meyn, S.P., Tweedie, R.L., 1993. Markov Chains and Stochastic Stability. Springer, London Ltd., London.
14. Mokkadem, A., 1987. Sur un modèle autorégressif non linéaire: ergodicité et ergodicité géométrique. J. Time Ser. Anal. 8 (2), 195-204.
15. Robert, C.P., Casella, G., 1999. Monte Carlo statistical methods. Springer, New York.
16. Roberts, G.O., Tweedie, R.L., 1996. Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 (1), 95-110.
17. Roberts, G.O., Tweedie, R.L., 1999. Bounds on regeneration times and convergence rates for Markov Chains. Stochastic Process. Appl. 80 (2), 211-229.
18. Roberts, G.O., Tweedie, R.L., 2001. Corrigendum to: "Bounds on regeneration times and convergence rates for Markov chains". Stochastic Process. Appl. 91 (2), 337-338.
19. Rosenthal, J.S., 1995a. Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Statist. Assoc. 90 (430), 558-566.
20. Rosenthal, J.S., 1995b. Correction: "Minorization conditions and convergence rates for Markov chain Monte Carlo". J. Amer. Statist. Assoc. 90 (431), 1136.
21. Rosenthal, J.S., 2001. A review of asymptotic convergence for general state space Markov Chains. Far East J. Math. Sci. 5, 37-50.
22. Stramer, O., Tweedie, R.L., 1999. Langevin-Type Models I: diffusions with given stationary distributions, and their discretizations. Methodol. Comput. Appl. Probab. 1 (3), 283-306.
23. Tanikawa, A., 1996. The rate of convergence of a homogeneous Markov chain arising from two-queue networks. Comput. Math. Appl. 31 (2), 103-109.
24. Tanikawa, A., 1999. Geometric ergodicity of nonlinear first order autoregressive models. Comm. Statist. Stochastic Models 15 (2), 227-245.
25. Tuominen, P., Tweedie, R.L., 1994. Subgeometric rates of convergence of f -ergodic Markov Chains. Adv. Appl. Probab. 26 (3), 775-798.
26. Tweedie, R.L., 1983. Criteria for rates of convergence of Markov chains, with application to queueing and storage theory. In: Kingman, J.F.C., Reuter, G.E.H. (Eds.), Probability, Statistics and Analysis. Cambridge University Press, Cambridge, pp. 260-276.
27. Veretennikov, A.Y., 2000. On polynomial mixing and the rate of convergence for stochastic difference and differential equations. Theory Probab. Appl. 44 (2), 361-374.