On the asymptotic normality of sequences of weak dependent random variables

Billingsley, P. (1968).Conbergence of Probability Measures, Wiley, New York.

Bradley, R. C. (1981). Central limit theorem under weak dependence.J. Multivar. Anal. 11, 1–16.

Bradley, R. C. (1992). On the spectral density and asymptotic normality of weakly dependent random fields.J. Theor. Prob. 5, 355–373.

Bradley, R. C. (1993). Equivalent mixing conditions for random fields.Ann. Prob. 21, 4, 1921-1926.

Bradley, R. C., and Utev, S. (1994). On second order properties of mixing random sequences and random fields. In Grigelionis, B.,et al. (eds.),Prob. Theory and Math. Stat., VSP/TEV, pp. 99–120.

Bryc, W., and Smolenski, W. (1993). Moment conditions for almost sure convergence of weakly correlated random variables.Proc. A.M.S. 119, 2, 629–635.

Doukhan, P., Massart, P., and Rio, E. (1994). The functional central limit theorem for strongly mixing processes.Ann. Inst. H. Poincaré 30, 1, 63–82.

Doukhan, P. (1994) Mixing Properties and Examples.Lecture Notes in Statistics Vol. 85, Springer-Verlag.

Ibragimov, I. A., and Linnik, Yu. V. (1971).Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen.

Ibragimov, I. A., and Rozanov, Y. A. (1978).Gaussian Random Processes, Springer-Verlag, Berlin.

Kolmogorov, A. N., and Rozanov, Y. A. (1960). On strong mixing conditions for stationary Gaussian processes.Theory Prob. Appl. 5, 204–208.

Miller, C. (1994a). Some theorems on stationary random fields with ap *-mixing condition. Ph.D. Thesis, Indiana University.

Miller, C. (1994b). Three theorems onp *-mixing random fields.J. of Theoretical Prob.,7, 4, 867–882.

Peligrad, M., and Utev, S. (1994). Central limit theorem for linear processes, to appear inAnn. Prob.

Peligrad, M. (1986a). Recent advances in the central limit theorem and its weak invariance principle for mixing sequences of random variables. In Eberlein, E., and Taqqu, M. (eds.),Progress in Prob. and Stat., Dependence in Prob. and Stat. 11, 193–224.

Peligrad, M. (1986b). Invariance principles under weak dependence.J. of Multiv. Anal. 19, 2, 229–310.

Peligrad, M. (1982). Invariance principles for mixing sequences of random variables.Ann. Prob. 10, 4, 968–981.

Utev, S. (1990). Central limit theorem for dependent random variables. In Grigelionis, B.,et al. (eds.),Prob. Theory and Math. Stat., VSP Mokslas2, 519–528.