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References

  1. Adamczak, Radosław. A tail inequality for suprema of unbounded empirical processes with applications to Markov chains. Electron. J. Probab. 13 (2008), no. 34, 1000--1034. MR2424985 (2009j:60032)
  2. Bennett, G. Probability inequalities for the sum of independant random variables. Journal of the American Statistician Association 57, 33--45.
  3. Bertail, P., and ClÈmenÁon, S. Sharp bounds for the tail of functionals of Markov chains. Theory Probab. Appl. 54 (2010) 505--515.
  4. Catoni, Olivier. Statistical learning theory and stochastic optimization.Lecture notes from the 31st Summer School on Probability Theory held in Saint-Flour, July 8–25, 2001.Lecture Notes in Mathematics, 1851. Springer-Verlag, Berlin, 2004. viii+272 pp. ISBN: 3-540-22572-2 MR2163920 (2006d:62004)
  5. Collet, P., Martinez, S., and Schmitt, B. Exponential inequalities for dynamical measures of expanding maps of the interval. Probability Theory and Related Fields 123, 301--322.
  6. Dedecker, Jérôme; Doukhan, Paul; Lang, Gabriel; León R., José Rafael; Louhichi, Sana; Prieur, Clémentine. Weak dependence: with examples and applications.Lecture Notes in Statistics, 190. Springer, New York, 2007. xiv+318 pp. ISBN: 978-0-387-69951-6 MR2338725 (2009a:62009)
  7. Dedecker, Jérôme; Prieur, Clémentine. New dependence coefficients. Examples and applications to statistics. Probab. Theory Related Fields 132 (2005), no. 2, 203--236. MR2199291 (2007b:62081)
  8. Dedecker, Jérôme; Prieur, Clémentine; Raynaud De Fitte, Paul. Parametrized Kantorovich-Rubinštein theorem and application to the coupling of random variables. Dependence in probability and statistics, 105--121, Lecture Notes in Statist., 187, Springer, New York, 2006. MR2283252 (2008c:60002)
  9. Doukhan, Paul. Mixing.Properties and examples.Lecture Notes in Statistics, 85. Springer-Verlag, New York, 1994. xii+142 pp. ISBN: 0-387-94214-9 MR1312160 (96b:60090)
  10. Doukhan, Paul; Louhichi, Sana. A new weak dependence condition and applications to moment inequalities. Stochastic Process. Appl. 84 (1999), no. 2, 313--342. MR1719345 (2001j:60033)
  11. Doukhan, P., and Neumann, M. A Bernstein type inequality for times series. Stoch. Proc. Appl. 117-7, 878--903.
  12. Doukhan, Paul; Wintenberger, Olivier. Weakly dependent chains with infinite memory. Stochastic Process. Appl. 118 (2008), no. 11, 1997--2013. MR2462284 (2010c:62281)
  13. Ibragimov, I. A. Some limit theorems for stationary processes.(Russian) Teor. Verojatnost. i Primenen. 7 1962 361--392. MR0148125 (26 #5634)
  14. Ibragimov, I. A.; Linnik, Yu. V. Independent and stationary sequences of random variables.With a supplementary chapter by I. A. Ibragimov and V. V. Petrov.Translation from the Russian edited by J. F. C. Kingman.Wolters-Noordhoff Publishing, Groningen, 1971. 443 pp. MR0322926 (48 #1287)
  15. Joulin, A., and Ollivier, Y. Curvature, concentration, and error estimates for Markov chain Monte Carlo. Ann. Probab. 38, 2418--2442.
  16. Lezaud, Pascal. Chernoff-type bound for finite Markov chains. Ann. Appl. Probab. 8 (1998), no. 3, 849--867. MR1627795 (99f:60061)
  17. Massart, Pascal. Concentration inequalities and model selection.Lectures from the 33rd Summer School on Probability Theory held in Saint-Flour, July 6–23, 2003.With a foreword by Jean Picard.Lecture Notes in Mathematics, 1896. Springer, Berlin, 2007. xiv+337 pp. ISBN: 978-3-540-48497-4; 3-540-48497-3 MR2319879 (2010a:62008)
  18. Merlevede, F., Peligrad, M., and Rio, E. Bernstein inequality and moderate deviations under strong mixing conditions. In High Dimensional Probability V: The Luminy Volume (Beachwood, Ohio, USA: IMS, 2009) C. HoudrÈ, V. Koltchinskii, D.M. Mason and M. Peligrad, Eds., 273--292..
  19. Merlevede, F., Peligrad, M., and Rio, E. A Bernstein type inequality and moderate deviations for weakly dependent sequences. Probab. Theory Related Fields DOI: 10.1007/s00440-010-0304-9.
  20. Nummelin, E. A splitting technique for Harris recurrent Markov chains. Z. Wahrsch. Verw. Gebiete 43 (1978), no. 4, 309--318. MR0501353 (58 #18732)
  21. Rio, Emmanuel. Sur le théorème de Berry-Esseen pour les suites faiblement dépendantes.(French) [The Berry-Esseen theorem for weakly dependent sequences] Probab. Theory Related Fields 104 (1996), no. 2, 255--282. MR1373378 (96k:60061)
  22. Rio, Emmanuel. Inégalités de Hoeffding pour les fonctions lipschitziennes de suites dépendantes.(French) [Hoeffding inequalities for Lipschitz functions of dependent sequences] C. R. Acad. Sci. Paris Sér. I Math. 330 (2000), no. 10, 905--908. MR1771956 (2001c:60034)
  23. Samson, Paul-Marie. Concentration of measure inequalities for Markov chains and $\Phi$-mixing processes. Ann. Probab. 28 (2000), no. 1, 416--461. MR1756011 (2001d:60015)
  24. Viennet, Gabrielle. Inequalities for absolutely regular sequences: application to density estimation. Probab. Theory Related Fields 107 (1997), no. 4, 467--492. MR1440142 (98f:62113)
  25. Walters, Peter. An introduction to ergodic theory.Graduate Texts in Mathematics, 79. Springer-Verlag, New York-Berlin, 1982. ix+250 pp. ISBN: 0-387-90599-5 MR0648108 (84e:28017)
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