H. Albrecher, C. Constantinescu, and S. Loisel, Explicit ruin formulas for models with dependence among risks, Insurance: Mathematics and Economics, vol.48, issue.2, pp.265-270, 2011.
DOI : 10.1016/j.insmatheco.2010.11.007
URL : https://hal.archives-ouvertes.fr/hal-00540621

S. Asmussen, Risk theory in a markovian environment, Scandinavian Actuarial Journal, vol.2, pp.69-100, 1989.

J. M. Bardet, P. Doukhan, G. Lang, and R. N. , Dependent Lindeberg central limit theorem and some applications. ESAIM Probab, Stat, vol.12, pp.154-172, 2008.
DOI : 10.1051/ps:2007053
URL : https://hal.archives-ouvertes.fr/hal-01197592

S. N. Bernstein, Sur l'extension du th???or???me limite du calcul des probabilit???s aux sommes de quantit???s d???pendantes, Mathematische Annalen, vol.97, issue.1, pp.1-59, 1927.
DOI : 10.1007/BF01447859

P. Billingsley, Convergence of probability measures, Wiley, p.1700749, 1968.
DOI : 10.1002/9780470316962

J. R. Blum, D. L. Hanson, and L. H. Koopmans, On the strong law of large numbers for a class of stochastic processes, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.137, issue.1, pp.1-11, 1963.
DOI : 10.1007/BF00535293

R. C. Bradley and W. Bryc, Multilinear forms and measures of dependence between random variables, Journal of Multivariate Analysis, vol.16, issue.3, pp.335-367, 1985.
DOI : 10.1016/0047-259X(85)90025-9

R. C. Bradley, Basic properties of strong mixing conditions. Dependence in probability and statistics, Progr. Probab. Statist, vol.11, pp.165-192, 1986.

R. C. Bradley, Basic properties of strong mixing conditions. A survey and some open questions. Update of, and a supplement to, the 1986 original. Probability Surveys, pp.107-144, 2005.

R. C. Bradley, Introduction to Strong Mixing Conditions, 2007.

C. Constantinescu, E. Hashorva, and L. Ji, Archimedean copulas in finite and infinite dimensions???with application to ruin problems, Insurance: Mathematics and Economics, vol.49, issue.3, pp.487-495, 2011.
DOI : 10.1016/j.insmatheco.2011.08.006

H. Cossette, P. Gaillardetz, and E. Marceau, Common mixture in the individual risk model. Mitteilungen der Schweiz, Aktuarvereinigung, vol.2, pp.131-157, 2002.

H. Cossette, L. David, and E. Marceau, Compound binomial risk model in a markovian environment, Insurance: Mathematics and Economics, vol.35, issue.2, pp.425-443, 2004.
DOI : 10.1016/j.insmatheco.2004.07.009

C. Coulon-prieur and P. Doukhan, A triangular central limit theorem under a new weak dependence condition, Statistics & Probability Letters, vol.47, issue.1, pp.61-68, 2000.
DOI : 10.1016/S0167-7152(99)00138-8

Y. A. Davydov, The Convergence of distributions generated by stationary stochastic processes. Theory of Probability and Its Application, pp.691-696, 1968.

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

J. Dedecker, P. Doukhan, G. Lang, R. León, J. R. Louhichi et al., Weak dependence, Lecture Notes in Statistics, 2007.
DOI : 10.1007/978-0-387-69952-3_2
URL : https://hal.archives-ouvertes.fr/hal-00686031

J. Dedecker and C. Prieur, New dependence coefficients. Examples and applications to statistics, Probability Theory and Related Fields, vol.95, issue.2, pp.203-236, 2005.
DOI : 10.1007/s00440-004-0394-3

P. Doukhan, Mixing properties and examples. Lecture note in statistics, p.85, 1994.

P. Doukhan and S. Louhichi, A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, pp.313-342, 1999.

W. Dziubdziela, Limit laws for kth order statistics from conditionally mixing arrays of random variables, Journal of Applied Probability, vol.51, issue.03, pp.679-687, 1986.
DOI : 10.1214/aoms/1177703551

H. U. Gerber, Mathematical fun with the compound binomial process. ASTIN Bull, pp.161-168, 1988.

M. I. Gordin, On the central limit theorem for stationary random processes, Dokl. Akad. Nauk. SSSR, vol.188, pp.739-741, 1969.

M. I. Gordin, A Note on the Martingale Method of Proving the Central Limit Theorem for Stationary Sequences, Journal of Mathematical Sciences, vol.44, issue.3, 2006.
DOI : 10.1007/s10958-006-0036-7

P. Hall and C. C. Heyde, Martingale limit theory and its application. Probability and Mathematical Statistics, 1980.

I. A. Ibragimov, Some limit theorems for stationary processes. Theory of Probability and its Applications, pp.349-382, 1962.

I. A. Ibragimov and Y. U. Linnik, Independent and stationary sequences of random variables, Groningen, pp.443-0322926, 1971.

Y. M. Kabanov, Hedging and liquidation under transaction costs in currency markets, Finance and Stochastics, vol.3, issue.2, pp.237-248, 2009.
DOI : 10.1007/s007800050061

M. Kacem, S. Loisel, and V. Maume-deschamps, Self normalized central limit theorems for conditionally independent variables and applications to risk processes

A. N. Kolmogorov and J. A. Rozanov, On a strong mixing condition for stationary Gaussian processes. Theory Of Probability and Its Applications, pp.204-208, 1960.

D. L. Mcleish, Invariance principles for dependent variables, Zeitschrift f???r Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol.5, issue.2, pp.165-178, 1975.
DOI : 10.1007/BF00532611

F. Merlevède, M. Peligrad, and S. Utev, Recent advances in invariance principles for stationary sequences, Probability Surveys, vol.3, issue.0, pp.1-36, 2006.
DOI : 10.1214/154957806100000202

G. L. Obrein, Limit theorems for sums of chain-dependent processes, Journal of applied probability, issue.11, pp.582-587, 1974.

M. Peligrad, Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables. Dependence in probability and statistics (Oberwolfach,1985), Progress Probab. Statist, vol.11, pp.193-223, 1986.

W. Philipp and W. F. Stout, Almost sure invariance principles for partial sums of weakly dependent random variables. Memoirs of the, pp.140-0433597, 1975.

P. Rao, Conditional independence, conditional mixing and conditional association, Annals of the Institute of Statistical Mathematics, vol.61, pp.441-460, 2009.

E. Rio, Covariance inequalities for strongly mixing processes, Ann. Inst. H. Poincaré Probab. Statist, vol.29, pp.587-597, 1993.

E. Rio, Inégalités de moments pour les suites stationnaires et fortement mélangeantes, C. R. Acad. Sci. Paris Sér. I Math, pp.318-355, 1994.

M. Rosenblatt, A central limit theorem and a strong mixing condition Proceeding national academy of Sciences of the United States of America, pp.427-433, 1956.

A. Veijanen, On conditionally mixing processes, Statistics & Probability Letters, vol.9, issue.1, pp.59-65, 1990.
DOI : 10.1016/0167-7152(90)90096-P