Free Access
Volume 19, 2015
Page(s) 440 - 481
Published online 11 November 2015
  1. R. Adamczak, A tail inequality for suprema of unbounded empirical processes with applications to Markov chains. Electron. J. Probab. 13 (2008) 1000–1034. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Adamczak and W. Bednorz, Orlicz integrability of additive functionals of Harris ergodic Markov chains. To Appear in High Dimensional Probability VII. Cargèse Volume. Preprint arXiv:1201.3567 (2012). [Google Scholar]
  3. K.B. Athreya and P. Ney, A new approach to the limit theory of recurrent Markov chains. Trans. Amer. Math. Soc. 245 (1978) 493–501. [CrossRef] [MathSciNet] [Google Scholar]
  4. J. Bae and S. Levental, Uniform CLT for Markov Chains and Its Invariance Principle: A Martingale Approach. J. Theoret. Probab. 8 (1995) 549–570. [CrossRef] [MathSciNet] [Google Scholar]
  5. P.H. Baxendale, Renewal theory and computable convergence rates for geometrically ergodic Markov chains. Ann. Appl. Probab. 15 (2005) 700–738. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Bertail and S. Clémencon, Sharp bounds for the tails of functionals of Markov chains. Teor. Veroyatost. Primenen. 54 (2009) 609–619; translation in Theory Probab. Appl. 54 (2010) 505–515. [CrossRef] [Google Scholar]
  7. A.A. Borovkov, Estimates for the distribution of sums and maxima of sums of random variables when the Cramér condition is not satisfied. Sib. Math. J. 41 (2000) 811–848. [CrossRef] [Google Scholar]
  8. A.A. Borovkov, Probabilities of large deviations for random walks with semi-exponential distributions. Sib. Math. J. 41 (2000) 1061–1093. [CrossRef] [Google Scholar]
  9. O. Bousquet, Concentration Inequalities for Sub-additive Functions Using the Entropy Method, Stochastic Inequalities and Applications. Progr. Probab. Springer, Basel (2003). [Google Scholar]
  10. J.-R. Chazottes and F. Redig, Concentration inequalities for Markov processes via coupling. Electron. J. Probab. 14 (2009) 1162–1180. [MathSciNet] [Google Scholar]
  11. X. Chen, Limit theorems for functionals of ergodic Markov chains with general state space. Mem. Amer. Math. Soc. 139 (1999) 664, [Google Scholar]
  12. S. Clémencon, Moment and probability inequalities for sums of bounded additive functionals of regular Markov chains via the Nummelin splitting technique. Statist. Probab. Lett. 55 (2001) 227–238. [CrossRef] [MathSciNet] [Google Scholar]
  13. R. Douc, G. Fort, E. Moulines and P. Soulier, Practical Drift Conditions for Subgeometric Rates of Convergence. Ann. Appl. Probab. 14 (2004) 1353–1377. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Douc, A. Guillin and E. Moulines, Bounds on regeneration times and limit theorems for subgeometric Markov chains. Ann. Inst. Henri Poincaré, Probab. Stat. 44 (2008) 239–257. [CrossRef] [MathSciNet] [Google Scholar]
  15. U. Einmahl and D. Li, Characterization of LIL behavior in Banach space. Trans. Amer. Math. Soc. 360 (2008) 6677–6693. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Fort and E. Moulines, Convergence of the Monte Carlo expectation maximization for curved exponential families. Ann. Statist. 31 (2003) 1220–1259. [CrossRef] [MathSciNet] [Google Scholar]
  17. F. Gao, A. Guillin and L. Wu, Bernstein type’s concentration inequalities for symmetric Markov processes. Teor. Veroyatnost. i Primenen. 58 (2013) 521–549 [CrossRef] [Google Scholar]
  18. S.F. Jarner and E. Hansen, Geometric ergodicity of Metropolis algorithms. Stoch. Proc. Appl. 85 (2000) 341–361 [CrossRef] [Google Scholar]
  19. A.A. Johnson and G.L. Jones, Gibbs Sampling for a Bayesian Hierarchical General Linear Model. Electron. J. Stat. 4 (2010) 313–333. [CrossRef] [MathSciNet] [Google Scholar]
  20. G.L. Jones and J.P. Hobert, Sufficient burn-in for Gibbs samplers for a hierarchical random effects model. Ann. Statist. 32 (2004) 784–817. [CrossRef] [MathSciNet] [Google Scholar]
  21. P. Kevei and D. Mason, A More General Maximal Bernstein Type Inequality. High Dimensional Probability VI. The Banff Volume. Vol. 66 of Progr. Probab. Birkhäuser (2013). [Google Scholar]
  22. T. Klein and E. Rio, Concentration around the mean for maxima of empirical processes. Ann. Probab. 33 (2005) 1060–1077. [CrossRef] [MathSciNet] [Google Scholar]
  23. L. Kontorovich and K. Ramanan, Concentration inequalities for dependent random variables via the martingale method. Ann. Probab. 36 (2008) 2126–2158. [CrossRef] [MathSciNet] [Google Scholar]
  24. I. Kontoyiannis and S.P. Meyn, Geometric ergodicity and the spectral gap of non-reversible Markov chains. Probab. Theory Related Fields 154 (2012) 327–339. [CrossRef] [MathSciNet] [Google Scholar]
  25. I. Kontoyiannis and S.P. Meyn, Spectral Theory and Limit Theorems for Geometrically Ergodic Markov Processes. Ann. Appl. Probab. (2003) 304–362. [Google Scholar]
  26. I. Kontoyiannis and S.P. Meyn, Large Deviations Asymptotic and the Spectral Theory of Multiplicatively Regular Markov Processes. Electron. J. Probab. 10 (2005) 61–123. [Google Scholar]
  27. K. Łatuszyński, B. Miasojedow and W. Niemiro, Nonasymptotic bounds on the estimation error of MCMC algorithms. Bernoulli 19 (2013) 2033–2066. [CrossRef] [MathSciNet] [Google Scholar]
  28. M. Ledoux and M. Talagrand, Probability in Banach spaces. Isoperimetry and processes. In vol. 23 of Results in Math. and Rel. Areas. Springer-Verlag, Berlin (1991). [Google Scholar]
  29. S. Levental, Uniform limit theorems for Harris recurrent Markov chains, Probab. Theory Relat. Fields 80 (1988) 101–118. [CrossRef] [Google Scholar]
  30. P. Lezaud, Chernoff and Berry-Esseen inequalities for Markov processes. ESAIM: PS 5 (2001) 183–201. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  31. K.L. Mengersen and R.L. Tweedie, Rates of convergence of the Hastings and Metropolis Algorithms. Ann. Statist. 24 (1996) 101–121. [CrossRef] [MathSciNet] [Google Scholar]
  32. K. Marton, A measure concentration inequality for contracting Markov chains. Geom. Funct. Anal. 6 (1996) 556–571. [CrossRef] [MathSciNet] [Google Scholar]
  33. F. Merlevede, M. Peligrad and E. Rio, A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probab. Theory Relat. Fields 151 (2011) 435–474. [CrossRef] [Google Scholar]
  34. S.P. Meyn, R.L. Tweedie, Markov Chains and Stochastic Stability. Communications and Control Engineering Series. Springer-Verlag, Ltd., London (1993). [Google Scholar]
  35. E. Nummelin, A splitting technique for Harris recurrent Markov chains. Z. Wahrsch. Verw. Gebiete 43 (1978) 309–318. [Google Scholar]
  36. E. Nummelin, General Irreducible Markov Chains and Non-Negative Operators. Cambridge Univ. Press. (1984). [Google Scholar]
  37. J.W. Pitman, An Identity for Stopping Times of a Markov Process. In Stud. Probab. Stat. (papers in honour of Edwin J. G. Pitman). North-Holland, Amsterdam (1976) 41–57. [Google Scholar]
  38. J.W. Pitman, Occupation measures for Markov chains. Adv. Appl. Probab. 9 (1977) 69–86. [CrossRef] [Google Scholar]
  39. D. Revuz and M. Yor, Continuous Martingales and Brownian motion, 3rd edition. Springer-Verlag (2005). [Google Scholar]
  40. E. Rio, Processus empiriques absolument réguliers et entropie universelle. Probab. Theory Relat. Fields 111 (1998) 585–608. [CrossRef] [Google Scholar]
  41. E. Rio, Inégalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes. C. R. Acad. Sci. Paris Sér. I Math. 330 (2000) 905–908. [CrossRef] [MathSciNet] [Google Scholar]
  42. G.O. Roberts and R.L. Tweedie, Geometric convergence and central limit theorems for multidimensional Hastings and Metropolis algorithms. Biometrika 83 (1996) 95–110. [CrossRef] [MathSciNet] [Google Scholar]
  43. P.M. Samson, Concentration of measure inequalities for Markov chains and Φ-mixing processes. Ann. Probab. 28 (2000) 416–461. [CrossRef] [MathSciNet] [Google Scholar]
  44. M. Talagrand, New concentration inequalities in product spaces. Invent. Math. (1996) 503–563. [Google Scholar]
  45. S. van de Geer and J. Lederer, The Bernstein-Orlicz norm and deviation inequalities. Probab. Theory Relat. Fields 157 (2013) 225–250. [CrossRef] [Google Scholar]
  46. A.W. van der Vaart and J.A. Wellner, Weak Convergence and Empirical Processes. With Applications to Statistics. Springer Ser. Stat. Springer-Verlag, New York (1996). [Google Scholar]
  47. O. Wintenberger, Deviation inequalities for sums of weakly dependent time series. Electron. Commun. Probab. 15 (2010) 489–503. [MathSciNet] [Google Scholar]
  48. O. Wintenberger, Weak transport inequalities and applications to exponential and oracle inequalities. Preprint arXiv:1207.4951v2 (2014). [Google Scholar]

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