Free Access
Issue
ESAIM: PS
Volume 5, 2001
Page(s) 183 - 201
DOI https://doi.org/10.1051/ps:2001108
Published online 15 August 2002
  1. D. Aldous and J. Fill, Reversible Markov Chains and Random Walks on Graphs. Monograph in preparation. Available from the Aldous's home page at http://www.stat.berkeley.edu/users/aldous/book.html
  2. B. Bercu and A. Rouault, Sharp large deviations for the Ornstein-Uhlenbeck process (to appear).
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  5. M.F. Cheng and F.Y. Wang, Estimation of spectral gap for elliptic operators. Trans. AMS 349 (1997) 1239-1267. [CrossRef] [MathSciNet]
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  7. J.D. Deuschel and D.W. Stroock, Large Deviations. Academic Press, Boston (1989).
  8. P. Diaconis, S. Holmes and R.M. Neal, Analysis of a non-reversible markov chain sampler, Technical Report. Cornell University, BU-1385-M, Biometrics Unit (1997).
  9. I.H. Dinwoodie, A probability inequality for the occupation measure of a reversible Markov chain. Ann. Appl. Probab 5 (1995) 37-43. [CrossRef] [MathSciNet]
  10. I.H. Dinwoodie, Expectations for nonreversible Markov chains. J. Math. Ann. App. 220 (1998) 585-596. [CrossRef]
  11. I.H. Dinwoodie and P Ney, Occupation measures for Markov chains. J. Theoret. Probab. 8 (1995) 679-691. [CrossRef] [MathSciNet]
  12. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 2. Wiley & Sons, 2nd Edition (1971).
  13. S. Gallot and D. Hulin and J. Lafontaine, Riemannian Geometry. Springer-Verlag (1990).
  14. D. Gillman, Hidden Markov Chains: Rates of Convergence and the Complexity of Inference, Ph.D. Thesis. Massachusetts Institute of Technology (1993).
  15. L. Gross, Logarithmic Sobolev Inequalities and Contractivity Properties of Semigroups, in Dirichlet forms, Varenna (Italy). Springer-Verlag, Lecture Notes in Math. 1563 (1992) 54-88.
  16. J.L. Jensen, Saddlepoint Approximations. Oxford Statist. Sci. Ser. 16.
  17. T. Kato, Perturbation theory for linear operators. Springer (1966).
  18. D. Landers and L. Rogge, On the rate of convergence in the central limit theorem for Markov chains. Z. Wahrscheinlichkeitstheorie Verw. 35 (1976) 169-183.
  19. G.F. Lawler and A.D. Sokal, Bounds on the L2 spectrum for Markov chains and Markov processes: A generalization of Cheeger's inequality. Trans. Amer. Math. Soc. 309 (1988) 557-580. [MathSciNet]
  20. P. Lezaud, Chernoff-type Bound for Finite Markov Chains. Ann. Appl. Probab 8 (1998) 849-867. [CrossRef] [MathSciNet]
  21. B. Mann, Berry-Esseen Central Limit Theorem for Markov chains, Ph.D. Thesis. Harvard University (1996).
  22. K. Marton, A measure concentration inequality for contracting Markov chains. Geom. Funct. Anal. 6 (1996) 556-571. [CrossRef] [MathSciNet]
  23. S.V. Nagaev, Some limit theorems for stationary Markov chains. Theory Probab. Appl. 2 (1957) 378-406. [CrossRef]
  24. P.M. Samson, Concentration of measure inequalities for Markov chains and Φ-mixing processes, Ann. Probab. 28 (2000) 416-461.
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  26. F.Y. Wang, Existence of spectral gap for elliptic operators. Math. Sci. Res. Inst. (1998).

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