References

1. S. Asmussen. Applied Probability and Queues. John Wiley & Sons, New York, 1987. Math. Review MR1978607 (2004f:60001)
2. S.K. Basu. A local limit theorem for attraction to the standard normal law: The case of infinite variance. Metrika 31 (1984), 245--252. Math. Review MR0754965 (86b:60033)
3. P. Billingsley. Convergence of Probability Measures. Wiley, New York, 1968. Math. Review MR0233396 (38 #1718)
4. M. Breth, J.S. Maritz, and E. J. Williams. On Distribution-Free Lower Confidence Limits for the Mean of a Nonnegative Random Variable. Biometrika 65 (1978), 529--534.
5. K.S. Chan and C.J. Geyer, Discussion paper. Ann. Stat. 22 (1994), 1747--1758.
6. X. Chen. Limit theorems for functionals of ergodic Markov chains with general state space. Mem. Amer. Math. Soc. 139 (1999). Math. Review MR1491814 (99k:60170)
7. W. Feller. An introduction to Probability Theory and its applications, Vol. II, 2nd ed. Wiley & Sons, New York, 1971. Math. Review MR0270403 (42 #5292)
8. C.J. Geyer. Practical Markov chain Monte Carlo. Stat. Sci. 7 (1992), 473-483.
9. O. H‰ggstrˆm. On the central limit theorem for geometrically ergodic Markov chains. Probab. Th. Relat. Fields 132 (2005), 74--82. Math. Review MR2136867 (2005m:60155)
10. J.P. Hobert, G.L. Jones, B. Presnell, and J.S. Rosenthal. On the Applicability of Regenerative Simulation in Markov Chain Monte Carlo. Biometrika 89 (2002), 731--743. Math. Review MR1946508 (2003m:60200)
11. I.A. Ibragimov and Y.V. Linnik. Independent and Stationary Sequences of Random Variables. Wolters-Noordhoff, Groningen (English translation), 1971. Math. Review MR0322926 (48 #1287)
12. G.L. Jones. On the Markov chain central limit theorem. Prob. Surveys 1 (2004), 299--320. Math. Review MR2068475 (2005j:60137)
13. C. Kipnis and S.R.S. Varadhan. Central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104 (1986), 1--19. Math. Review MR0834478 (87i:60038)
14. S.P. Meyn and R.L. Tweedie. Markov chains and stochastic stability. Springer-Verlag, London, 1993. Math. Review MR1287609 (95j:60103)
15. P.A. Mykland, L. Tierney, and B. Yu. Regeneration in Markov chain samplers. J. Amer. Stat. Assoc. 90 (1995), 233--241.
16. M. Peligrad. Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables (a survey). In Dependence in Probability and Statistics: A Survey of Recent Results, E. Eberlein and M.S. Taqqu, eds., Birkhauser, Cambridge, Mass., 1986, pp. 193--223. Math. Review MR0899991 (88j:60053)
17. G.O. Roberts. A note on acceptance rate criteria for CLTs for Metropolis-Hastings algorithms. J. Appl. Prob. 36 (1999), 1210--1217. Math. Review MR1742161 (2001a:60083)
18. G.O. Roberts and J.S. Rosenthal. Geometric ergodicity and hybrid Markov chains. Electronic Comm. Prob. 2 (1997), 13--25. Math. Review MR1448322 (99b:60122)
19. G.O. Roberts and J.S. Rosenthal. General state space Markov chains and MCMC algorithms. Prob. Surveys 1 (2004), 20--71. Math. Review MR2095565 (2005i:60135)
20. G.O. Roberts and J.S. Rosenthal. Variance Bounding Markov Chains. Preprint, 2006.
21. J.S. Rosenthal. A review of asymptotic convergence for general state space Markov chains. Far East J. Theor. Stat. 5 (2001), 37--50. Math. Review MR1848443 (2002m:60130)
22. W. Rudin. Functional Analysis, 2nd ed. McGraw-Hill, New York, 1991. Math. Review MR1157815 (92k:46001)
23. L. Tierney. Markov chains for exploring posterior distributions (with discussion). Ann. Stat. 22 (1994), 1701--1762. Math. Review MR1329166 (96m:60150)