D. W. Andrews, Non-strong mixing autoregressive processes, Journal of Applied Probability, vol.21, issue.04, pp.930-934, 1984.
DOI : 10.2307/3212764

H. Berbee, Chains with infinite connections: uniqueness and Markov representation. Probab. Theory Related Fields, pp.243-253, 1987.

P. Bougerol, Kalman filtering with random coefficients and contractions. Probab. Theory Related Fields, pp.942-959, 1993.

P. Bühlmann and A. J. Wyner, Variable length Markov chains, Ann. Statist, vol.27, issue.2, pp.480-513, 1999.

F. Comets, R. Fernández, and P. A. Ferrari, Processes with long memory: Regenerative construction and perfect simulation, The Annals of Applied Probability, vol.12, issue.3, pp.921-943, 2002.
DOI : 10.1214/aoap/1031863175

URL : http://arxiv.org/abs/math/0009204

J. Dedecker and P. Doukhan, A new covariance inequality and applications. Stochastic Process, Appl, vol.106, issue.1, pp.63-80, 2003.

J. Dedecker, P. Doukhan, G. Lang, J. R. León, S. Louhichi et al., Weak Dependence, Examples and Applications, Lecture Notes in Statistics, vol.190, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00686031

J. Dedecker and C. Prieur, Coupling for ?-Dependent Sequences and Applications, Journal of Theoretical Probability, vol.3, issue.4, pp.861-855, 2004.
DOI : 10.1007/s10959-004-0578-x

P. Diaconis and D. Freedman, Iterated Random Functions, SIAM Review, vol.41, issue.1, pp.45-76, 1999.
DOI : 10.1137/S0036144598338446

R. L. Dobrushin, Prescribing a System of Random Variables by Conditional Distributions, Theory of Probability & Its Applications, vol.15, issue.3, pp.458-486, 1970.
DOI : 10.1137/1115049

R. L. Dobrushin and S. Kusuoka, Statistical Mechanics and Fractals, Lecture Notes in Mathematics, vol.1567, 1993.
DOI : 10.1007/BFb0074238

P. Doukhan, Mixing, volume 85 of Lecture Notes in Statistics, 1994.

P. Doukhan and S. Louhichi, A new weak dependence condition and applications to moment inequalities. Stochastic Process, Appl, vol.84, issue.2, pp.313-342, 1999.

P. Doukhan, H. Madre, and M. Rosenbaum, Weak dependence for infinite ARCH-type bilinear models, Statistics, vol.26, issue.2, pp.31-45, 2007.
DOI : 10.1016/S0304-4149(99)00055-1

P. Doukhan, P. Massart, and E. Rio, The functional central limit theorem for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Statist, vol.30, issue.2, pp.63-82, 1994.

P. Doukhan, G. Teyssì, and P. Winant, A LARCH(???) Vector Valued Process, Dependence in Probability and Statistics, 2006.
DOI : 10.1007/0-387-36062-X_11

URL : https://hal.archives-ouvertes.fr/hal-00141714

M. Duflo, Random Iterative Models, Applications of Mathematics, vol.34, 1997.
DOI : 10.1007/978-3-662-12880-0

R. Fernández and G. Maillard, Chains with Complete Connections and One-Dimensional Gibbs Measures, Electronic Journal of Probability, vol.9, issue.0, pp.145-176, 2004.
DOI : 10.1214/EJP.v9-149

L. Giraitis, R. Leipus, P. M. Robinson, and D. Surgailis, LARCH, Leverage, and Long Memory, Journal of Financial Econometrics, vol.2, issue.2, pp.177-210, 2004.
DOI : 10.1093/jjfinec/nbh008

M. Iosifescu and S. Grigorescu, Dependence with Complete Connections and its Applications, volume 96 of Cambridge Tracts in Mathematics, 1990.

M. Iosifescu and R. Theodorescu, Random Processes and Learning, 1969.

M. Kac, Probability and Related Topics in Physical Sciences, volume 1a of Lectures in Applied Mathematics Series, 1959.

O. Kallenberg, Foundations of Modern Probability. Probability and its Applications, 1997.

M. A. Krasnoselskii and Y. B. Rutickii, Convex Functions and Orlicz Spaces, Noordhoff Ltd, 1961.

L. D. Landau and E. M. Lifshitz, Statistical Physics, volume 5 of Course of Theoretical Physics, 1980.

A. Latour, The Multivariate Ginar(p) Process, Advances in Applied Probability, vol.29, issue.01, pp.228-247, 1997.
DOI : 10.1214/aop/1176994950

F. Merlevde and M. Peligrad, On the Weak Invariance Principle for Stationary Sequences under Projective Criteria, Journal of Theoretical Probability, vol.32, issue.2, pp.647-689, 2006.
DOI : 10.1007/s10959-006-0029-y

M. Peligrad and S. Utev, A new maximal inequality and invariance principle for stationary sequences, The Annals of Probability, vol.33, issue.2, pp.798-815, 2005.
DOI : 10.1214/009117904000001035

N. Ragache and O. Wintenberger, Convergence rates for density estimators of weakly dependent time series, Dependence in Probability and Statistics, 2006.
DOI : 10.1007/0-387-36062-X_16

URL : https://hal.archives-ouvertes.fr/hal-00123500

E. Rio, Théorie asymptotique des processus aléatoires faiblement dépendants, of Mathématiques & Applications, 2000.

W. B. Wu, Nonlinear system theory: Another look at dependence, Proc. Natl. Acad. Sci. USA, pp.14150-14154, 2005.
DOI : 10.1073/pnas.0506715102

L. Laboratoire-de-statistique and J. Timbre, avenue Pierre Larousse, 92240 MALAKOFF, FRANCE E-mail address: doukhan@ensae.fr (2) SAMOS-MATISSE (Statistique Appliquée et MOdélisation Stochastique) Centre d' ´ Economie de la Sorbonne Université Paris 1 -Panthéon-Sorbonne