The PDF file you selected should load here if your Web browser has a PDF reader plug-in installed (for example, a recent version of Adobe Acrobat Reader).

Alternatively, you can also download the PDF file directly to your computer, from where it can be opened using a PDF reader. To download the PDF, click the Download link below.

If you would like more information about how to print, save, and work with PDFs, Highwire Press provides a helpful Frequently Asked Questions about PDFs.

Download this PDF file Fullscreen Fullscreen Off

References

  1. S. Asmussen (1987), Applied probability and queues. John Wiley & Sons, New York. Math Review link
  2. J. R. Baxter and J. S. Rosenthal (1995), Rates of convergence for everywhere-positive Markov chains. Stat. Prob. Lett. 22, 333-338. Math Review link
  3. R. N. Bhattacharya (1982), On the functional central limit theorem and the law of the iterated logarithm for Markov processes. Z. Wahrscheinlichkeitstheorie Verw. gebiete 60, 185-201. Math Review link
  4. R. Carmona and A. Klein (1983), Exponential moments for hitting times of uniformly ergodic Markov processes. Ann. Prob. 11, 648-655. Math Review link
  5. K. S. Chan and C. J. Geyer (1994), Discussion paper. Ann. Stat. 22, 1747-1758. Math Review article not available.
  6. J. B. Conway (1985), A course in functional analysis. Springer-Verlag, New York. Math Review link
  7. Y. Derriennic and M. Lin (1996), Sur le theoreme limite central de Kipnis et Varadhan pour les chaines reversibles ou normales. Comptes Rendus de l'Academie des Sciences, Serie I, 323, No. 9, 1053-1058. Math Review link
  8. J. L. Doob (1994), Measure theory. Springer-Verlag, New York. Math Review link
  9. S. Duane, A. D. Kennedy, B. J. Pendleton, and D. Roweth (1987), Hybrid Monte Carlo. Phys. Lett. B 195, 216-222. Math Review article not available.
  10. A. E. Gelfand and A. F. M. Smith (1990), Sampling based approaches to calculating marginal densities. J. Amer. Stat. Assoc. 85, 398-409. Math Review link
  11. C. Geyer (1992), Practical Markov chain Monte Carlo. Stat. Sci. 7, No. 4, 473-483. Math Review article not available.
  12. P. J. Green (1994), Reversible jump MCMC computation and Bayesian model determination. Tech. Rep., Dept. Mathematics, U. of Bristol. Math Review article not available.
  13. P. E. Greenwood, I. W. McKeague, and W. Wefelmeyer (1995), Outperforming the Gibbs sampler empirical estimator for nearest neighbour random fields. Tech. Rep., Dept. Mathematics, U. of British Columbia. Math Review article not available.
  14. W. K. Hastings (1970), Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. Math Review article not available.
  15. N. Jain and B. Jamison (1967), Contributions to Doeblin's theory of Markov processes. Z. Wahrsch. Verw. Geb. 8, 19-40. Math Review article not available.
  16. C. Kipnis and S. R. S. Varadhan (1986), central limit theorem for additive functionals of reversible Markov processes and applications to simple exclusions. Comm. Math. Phys. 104, 1-19. Math Review link
  17. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E. Teller (1953), Equations of state calculations by fast computing machines. J. Chem. Phys. 21, 1087-1091. Math Review article not available.
  18. S. P. Meyn and R. L. Tweedie (1993), Markov chains and stochastic stability, Springer-Verlag, London. Math Review link
  19. S. P. Meyn and R. L. Tweedie (1994), Computable bonds for convergence rates of Markov chains. Ann. Appl. Prob. 4, 981-1011. Math Review link
  20. R. M. Neal (1993), Probabilistic inference using Markov chain Monte Carlo methods. Tech. Rep. CRG-TR-93-1, Dept. Comp. Sci., U. of Toronto. Math Review article not available.
  21. E. Nummelin (1984), General irreducible Markov chains and non-negative operators. Cambridge University Press. Math Review link
  22. E. Nummelin and R. L. Tweedie (1978), Geometric ergodicity and $R$-positivity for general Markov chains. Ann. Prob. 6, 404-420. Math Review article not available.
  23. S. Orey (1971), Lecture notes on limit theorems for Markov chain transition probabilities. Van Nostrand Reinhold, London. Math Review article not available.
  24. M. Reed and B. Simon (1972), Methods of modern mathematical physics. Volume I: Functional analysis. Academic Press, New York. Math Review article not available.
  25. G. O. Roberts and R. L. Tweedie (1996), Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83, 95-110. Math Review link
  26. M. Rosenblatt (1962), Random Processes. Oxford University Press, New York. Math Review article not available.
  27. J. S. Rosenthal (1995), Minorization conditions and convergence rates for Markov chain Monte Carlo. J. Amer. Stat. Assoc. 90, 558-566. Math Review link
  28. R. L. Royden (1968), Real analysis, 2nd ed. MacMillan, New York. Math Review article not available.
  29. W. Rudin (1991), Functional Analysis, 2nd ed. McGraw-Hill, New York. Math Review link
  30. A. F. M. Smith and G. O. Roberts (1993), Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion). J. Roy. Stat. Soc. Ser. B 55, 3-24. Math Review link
  31. L. Tierney (1994), A note on Metropolis Hastings kernels for general state spaces. Tech. Rep. 606, School of Statistics, U. of Minnesota. Math Review link
  32. R. L. Tweedie (1978), Geometric ergodicity and $R$-positivity for general Markov chains. Ann. Prob. 6, 404-420. Math Review article not available.
  33. D. Vere-Jones (1962), Geometric ergodicity in denumerable Markov chains. Quart. J. Math. Oxford (2) 13, 7-28. Math Review article not available.
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.