Free Access
Volume 18, 2014
Page(s) 468 - 482
Published online 08 October 2014
  1. C. Ané, S. Blachère, D. Chafaï, P. Fougères, I. Gentil, F. Malrieu, C. Roberto and G. Scheffer, Sur les inégalités de Sobolev logarithmiques. Vol. 10 of Panoramas et Synthèses. Société Mathématique de France, Paris (2000). [Google Scholar]
  2. D. Bakry, P. Cattiaux and A. Guillin, Rate of convergence for ergodic continuous Markov processes: Lyapunov versus Poincaré. J. Func. Anal. 254 (2008) 727–759. [Google Scholar]
  3. K. Bartkiewicz, A. Jakubowski, T. Mikosch and O. Wintenberger, Stable limits for sums of dependent infinite variance random variables. Probab. Theory Relat. Fields 150 (2011) 337–372. [CrossRef] [Google Scholar]
  4. B. Basrak, D. Krizmanic and J. Segers, A functional limit theorem for dependent sequences with infinite variance stable limits. Ann. Probab. 40 (2012) 2008–2033. [CrossRef] [Google Scholar]
  5. P. Cattiaux, A pathwise approach of some classical inequalities. Potential Analysis 20 (2004) 361–394. [CrossRef] [MathSciNet] [Google Scholar]
  6. P. Cattiaux, D. Chafai and A. Guillin, Central Limit Theorem for additive functionals of ergodic Markov Diffusions. ALEA, Lat. Am. J. Probab. Math. Stat. 9 (2012) 337–382. [MathSciNet] [Google Scholar]
  7. P. Cattiaux and A. Guillin, Deviation bounds for additive functionals of Markov processes. ESAIM: PS 12 (2008) 12–29. [CrossRef] [EDP Sciences] [Google Scholar]
  8. P. Cattiaux and A. Guillin, Trends to equilibrium in total variation distance. Ann. Inst. Henri Poincaré. Prob. Stat. 45 (2009) 117–145. [CrossRef] [Google Scholar]
  9. P. Cattiaux, A. Guillin and C. Roberto, Poincaré inequality and the ?p convergence of semi-groups. Elec. Commun. Prob. 15 (2010) 270–280. [CrossRef] [Google Scholar]
  10. P. Cattiaux, A. Guillin and P.A. Zitt, Poincaré inequalities and hitting times. Ann. Inst. Henri Poincaré. Prob. Stat. 49 (2013) 95–118. [CrossRef] [Google Scholar]
  11. Mu-Fa Chen, Eigenvalues, inequalities, and ergodic theory. Probab. Appl. (New York). Springer-Verlag London Ltd., London (2005). [Google Scholar]
  12. R.A. Davis, Stable limits for partial sums of dependent random variables. Ann. Probab. 11 (1983) 262–269. [CrossRef] [Google Scholar]
  13. M. Denker and A. Jakubowski, Stable limit theorems for strongly mixing sequences. Stat. Probab. Lett. 8 (1989) 477–483. [CrossRef] [Google Scholar]
  14. A. Jakubowski, Minimal conditions in p-stable limit theorem. Stochastic Process. Appl. 44 (1993) 291–327. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Jara, T. Komorowski and S. Olla, Limit theorems for additive functionals of a Markov chain. Ann. Appl. Probab. 19 (2009) 2270–2300. [CrossRef] [Google Scholar]
  16. D. Krizmanic, Functional limit theorems for weakly dependent regularly varying time series. Ph.D. thesis (2010). Available at˜dkrizmanic/DKthesis.pdf. [Google Scholar]
  17. S.P. Meyn and R.L. Tweedie, Markov chains and stochastic stability. Commun. Control Eng. Series. Springer-Verlag London Ltd., London (1993). [Google Scholar]
  18. F. Merlevède, M. Peligrad and S. Utev, Recent advances in invariance principles for stationary sequences. Probab. Surv. 3 (2006) 1–36. [CrossRef] [MathSciNet] [Google Scholar]
  19. L. Miclo, On hyperboundedness and spectrum of Markov operators. Preprint, available on hal-00777146 (2013). [Google Scholar]
  20. M. Röckner and F.Y. Wang, Weak Poincaré inequalities and L2-convergence rates of Markov semi-groups. J. Funct. Anal. 185 (2001) 564–603. [CrossRef] [MathSciNet] [Google Scholar]
  21. M. Tyran-Kaminska, Convergence to Lévy stable processes under some weak dependence conditions. Stochastic Process. Appl. 120 (2010) 1629–1650. [CrossRef] [MathSciNet] [Google Scholar]
  22. E. Van Doorn and P. Schrdner, Geometric ergodicity and quasi-stationnarity in discrete time Birth-Death processes. J. Austral. Math. Soc. Ser. B 37 (1995) 121–144. [CrossRef] [MathSciNet] [Google Scholar]

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