A. N. Borodin and I. A. Ibragimov, Limit theorems for functionals of random walks, Transl. into English: Proc. Steklov Inst, p.195, 1994.

R. C. Bradley, On quantiles and the central limit question for strongly mixing sequences. Dedicated to Murray Rosenblatt, Journal of Theoretical Probability, vol.10, issue.2, pp.507-555, 1997.
DOI : 10.1023/A:1022624919588

B. M. Brown, Martingale Central Limit Theorems, The Annals of Mathematical Statistics, vol.42, issue.1, pp.59-66, 1971.
DOI : 10.1214/aoms/1177693494

X. Chen, Limit theorems for functionals of ergodic Markov chains with general state space. Memoirs of the AMS, p.664, 1999.

C. Cuny, POINTWISE ERGODIC THEOREMS WITH RATE WITH APPLICATIONS TO LIMIT THEOREMS FOR STATIONARY PROCESSES, Stochastics and Dynamics, vol.11, issue.01, pp.135-155, 2011.
DOI : 10.1142/S0219493711003206

C. Cuny and F. Merlevède, On martingale approximations and the quenched weak invariance principle, The Annals of Probability, vol.42, issue.2, 2012.
DOI : 10.1214/13-AOP856
URL : https://hal.archives-ouvertes.fr/hal-00745641

C. Cuny and M. Peligrad, Central Limit Theorem Started at a Point for??Stationary Processes and Additive Functionals of??Reversible Markov Chains, Journal of Theoretical Probability, vol.35, issue.1, pp.171-188, 2012.
DOI : 10.1007/s10959-010-0321-8

C. Cuny and D. Voln´yvoln´y, A quenched invariance principle for stationary processes. arXiv:1202.4875, accepted for publication in ALEA Lat, Am. J. Probab. Math. Stat, 2012.

J. Dedecker, S. Gouëzel, and F. Merlevède, Some almost sure results for unbounded functions of intermittent maps and their associated Markov chains, Annales de l'Institut Henri Poincar??, Probabilit??s et Statistiques, vol.46, issue.3, pp.46-796, 2010.
DOI : 10.1214/09-AIHP343
URL : https://hal.archives-ouvertes.fr/hal-00402864

J. Dedecker and F. Merlevède, Necessary and sufficient conditions for the conditional central limit theorem, The Annals of Probability, vol.30, issue.3, pp.1044-1081, 2002.
DOI : 10.1214/aop/1029867121

J. Dedecker and E. Rio, On the functional central limit theorem for stationary processes, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.36, issue.1, pp.1-34, 2000.
DOI : 10.1016/S0246-0203(00)00111-4

Y. Derriennic and M. Lin, The central limit theorem for Markov chains with normal transition operators, started at a point, Probability Theory and Related Fields, vol.119, issue.4, pp.508-528, 2001.
DOI : 10.1007/PL00008769

Y. Derriennic and M. Lin, The central limit theorem for Markov chains started at a point, Probab. Theory Relat, pp.125-73, 2003.

P. Doukhan, P. Massart, and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Statist, vol.30, pp.63-82, 1994.

O. Durieu, Independence of four projective criteria for the weak invariance principle, ALEA Lat. Am. J. Probab. Math. Stat, vol.5, pp.21-26, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00291499

O. Durieu and D. Voln´yvoln´y, Comparison between criteria leading to the weak invariance principle, Annales de l'Institut Henri Poincare (B) Probability and Statistics, vol.44, issue.2, pp.324-340, 2008.
DOI : 10.1214/07-AIHP123
URL : https://hal.archives-ouvertes.fr/hal-00291468

C. G. Esseen and S. Janson, On moment conditions for normed sums of independent variables and martingale differences, Stochastic Processes and their Applications, vol.19, issue.1, pp.173-182, 1985.
DOI : 10.1016/0304-4149(85)90048-1

M. I. Gordin, The central limit theorem for stationary processes, Soviet Math. Dokl, vol.10, pp.1174-1176, 1969.

M. I. Gordin, Abstracts of Communication, International Conference on Probability Theory, 1973.

M. I. Gordin and B. A. Lifsic, The central limit theorem for stationary Markov processes, Soviet Math. Dokl, vol.19, pp.392-394, 1978.

S. Gouëzel, Central limit theorem and stable laws for intermittent maps, Probability Theory and Related Fields, vol.128, issue.1, pp.82-122, 2004.
DOI : 10.1007/s00440-003-0300-4

C. C. Heyde and B. M. Brown, On the departure from normality of a certain class of martingales, Ann. Math. Statist, pp.41-2161, 1970.

U. Krengel, Ergodic theorems, de Gruyter Studies in Mathematics, 1985.

M. Maxwell and M. Woodroofe, Central limit theorem for additive fonctionals of Markov chains, Ann. Probab, vol.28, pp.713-724, 2000.

F. Merlevède, M. Peligrad, and S. Utev, Recent advances in invariance principles for stationary sequences. Probability Surveys, pp.1-36, 2006.

F. Merlevède, C. Peligrad, and M. Peligrad, Almost sure invariance principles via martingale approximation, Stochastic Processes and their Applications, vol.122, issue.1, pp.170-190, 2012.
DOI : 10.1016/j.spa.2011.09.004

F. Merlevède and E. Rio, Strong approximation of partial sums under dependence conditions with application to dynamical systems, Stochastic Processes and their Applications, vol.122, issue.1, pp.386-417, 2012.
DOI : 10.1016/j.spa.2011.08.012

S. P. Meyn and R. L. Tweedie, Markov chains and stochastic stability. Communications and Control Engineering Series, 1993.

M. Peligrad and S. Utev, Central limit theorem for stationary linear processes, The Annals of Probability, vol.34, issue.4, pp.1608-1622, 2006.
DOI : 10.1214/009117906000000179

Y. Pomeau and P. Manneville, Intermittent transition to turbulence in dissipative dynamical systems, Communications in Mathematical Physics, vol.20, issue.2, pp.189-197, 1980.
DOI : 10.1007/BF01197757

M. Rosenblatt, A CENTRAL LIMIT THEOREM AND A STRONG MIXING CONDITION, Proc. Natl. Acad. Set. USA, pp.43-47, 1956.
DOI : 10.1073/pnas.42.1.43

J. G. Sina?-i, A weak isomorphism of transformations with invariant measure, Dokl. Akad. Nauk SSSR, vol.147, pp.797-800, 1962.

D. Voln´yvoln´y and P. Samek, On the invariance principle and the law of iterated logarithm for stationary processes. Mathematical physics and stochastic analysis 424-438, 2000.

D. Voln´yvoln´y and M. Woodroofe, An example of non-quenched convergence in the conditional central limit theorem for partial sums of a linear process. Dependence in analysis, probability and number theory (The Phillipp memorial volume, pp.317-323, 2010.

D. Voln´yvoln´y and M. Woodroofe, Quenched central limit theorems for sums of stationary processes, 2010.

W. Wu and M. Woodroofe, Martingale approximations for sums of stationary processes, Ann. Probab, vol.32, pp.1674-1690, 2004.

O. Zhao and M. Woodroofe, Law of the iterated logarithm for stationary processes, The Annals of Probability, vol.36, issue.1, pp.127-142, 2008.
DOI : 10.1214/009117907000000079