Subgeometric ergodicity of strong Markov processes

Annals of Applied Probability

Volumn 15, Issue 2, 2005, Pages 1565-1589

  Fort, G ^a   Roberts, G O ^b  

^a CNRS   (France)

^b LANCASTER UNIVERSITY   (United Kingdom)

Author keywords

Drift criterion; Langevin diffusions; Markov processes; Storage models; Subgeometric f ergodicity

Indexed keywords

EID: 21244477580     PISSN: 10505164     EISSN: 10505164     Source Type: Journal    
DOI: 10.1214/105051605000000115     Document Type: Article

References (36)

1. BARNDORFF-NIELSEN, O. and SHEPHARD, N. (2001). Non-gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics. J, Roy. Stat. Soc., B 63 167-241.
2. DAI, J. and MEYN, S. (1995). Stability and convergence of moments for multiclass queuing networks via fluid limit models. IEEE Trans. Automat. Control 40 1889-1904.
3. DAVIS, M. (1993). Markov Models and Optimization. London: Chapman and Hall.
4. DOUC, R., FORT, G., MOULINES, E. and SOULIER, P. (2004). Practical drift conditions for subgeometric rates of convergence. Ann. Appl. Probab. 14 1353-1377.
5. DOWN, N., MEYN, S. and TWEEDIE, R. (1995). Exponential and uniform ergodicity of Markov processes. Ann. Probab. 23 1671-1691.
6. DYNKIN, E. (1965). Markov Processes. Springer; Academic Press.
7. FELLER, W. (1971). An introduction to probability theory and its applications. Vol. II. 2nd ed. John Wiley & Sons Inc., New York.
8. FORT, G. and MOULINES, E. (2003). Polynomial ergodicity of markov transition kernels. Stoc. Proc. Appl. 103 57-99.
9. GANIDIS, H., ROYNETTE, B. and SIMONOT, F. (1999). Convergence rate of semi-groups to their invariant probability. Stoc. Proc. Appl. 79 243-263.
10. GETOOR, R. (ed.) (1980). Transience and recurrence of Markov processes. 784, Lect. Notes Math. 397-409.
11. HAS'MINSKII, R. (1960). Ergodic properties of recurrent diffusion processes and stabilization of the solution to the Cauchy problem for parabolic equations. Theory Probab. Appl. 5 179-196.
12. HAS'MINSKII, R. (1980). Stochastic stability of differential equations. Sijthoff and Noordhoff.
13. JARNER, S. and ROBERTS, G. (2001). Convergence of heavy tailed MCMC algorithms. Tech. rep., Lancaster University. Available at //www.statslab.cam. ac.uk/mcmc.
14. JARNER, S. and ROBERTS, G. (2002). Polynomial convergence rates of Markov Chains. Ann. Appl. Prob. 12 224-247.
15. KENT, J. (1978). Time-reversible diffusions. Adv. Appl. Prob. 10 819-835.
16. KRASNOSEL'SKII, M. and RUTICKII, Y. (1961). Convex functions and Orlicz spaces. Noordhoff, Groningen.
17. 2 spectrum for Markov chains and Markov processes: a generalization of Cheeger's inequality. Trans. Amer. Math. Soc. 309 557-580.
18. LUND, R., MEYN, S. and TWEEDIE, R. (1996). Computable exponential convergence rates for stochastically ordered Markov processes. Ann. Appl. Prob. 6 218-237.
19. MALYSHKIN, M. (2001). Subexponential estimates of the rate of convergence to the invariant measure for stochastic differential equations. Theory Probab. Appl. 45 466-479.
20. MEYN, S. and TWEEDIE, R. (1993a). Generalized resolvents and Harris Recurrence of Markov processes. American Mathematical Society, Providence, RI, 227-250.
21. MEYN, S. P. and TWEEDIE, R. L. (1993b). Markov chains and stochastic stability. Springer- Verlag London Ltd., London.
22. MEYN, S. P. and TWEEDIE, R. L. (1993c). Stability of markovian processes II: continuous-time processes and sampled chains. Adv. Appl. Prob. 25 487-517.
23. MEYN, S. P. and TWEEDIE, R. L. (1993d). Stability of markovian processes III: Foster- Lyapunov criteria for continuous-time processes. Adv. Appl. Prob. 25 518-548.
24. NUMMELIN, E. (1984). General irreducible Markov chains and nonnegative operators. Cambridge University Press, Cambridge.
25. NUMMELIN, E. and TUOMINEN, P. (1983). The rate of convergence in Orey's theorem for Harris recurrent Markov chains with applications to renewal theory. Stoc. Proc. Appl. 15 295-311.
26. ROBERTS, G. and ROSENTHAL, J. (1996). Quantitative bounds for convergence rates of con- tinuous time Markov processes. Electronic J. Probab. 1 1-21.
27. ROBERTS, G. and STRAMER, O. (2003). Langevin diffusions and Metropolis-Hastings algo- rithms. To appear in Methodology and Computing in Applied Probability.
28. ROBERTS, G. and TWEEDIE, R. (1996). Exponential convergence of Langevin diffusions and their discrete approximations. Bernoulli 341-364.
29. ROBERTS, G. and TWEEDIE, R. (2000). Rates of convergence of stochastically monotone and continuous time Markov models. J. Appl. Probab. 37 359-373.
30. ROBERTS, G. and TWEEDIE, R. (2002). Understanding MCMC. To be published.
31. SHARPE, M. (1988). General theory of Markov Processes. Academic Press.
32. STRAMER, O. and TWEEDIE, R. (1999a). Langevin-type models I: Diffusions with given sta- tionary distributions, and their discretizations. Methodol. Comput. Appl. Probab. 1 283-306.
33. STRAMER, O. and TWEEDIE, R. (1999b). Langevin-type models II: Self-targeting candidates for MCMC algorithms. Methodol. Comput. Appl. Probab. 1 307-328.
34. THORISSON, H. (1985). The queue GI/G/1: finite moments of the cycle variables and uniform rates of convergence. Stoc. Proc. Appl. 19 83-99.
35. TUOMINEN, P. and TWEEDIE, R. (1994). Subgeometric rates of convergence of f-ergodic Markov Chains. Adv. in Appl. Probab. 26 775-798.
36. VERETENNIKOV, A. (1999). On polynomial mixing and convergence rate for stochastic difference and differential equations. Theory Probab. Appl. 44 361-374.