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Weak convergence of multidimensional empirical processes for strong mixing sequences of stochastic vectors. (English) Zbl 0304.60019


MSC:

60G10 Stationary stochastic processes
60F15 Strong limit theorems
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References:

[1] Bickel, P. J.; Wichura, M. J., Convergence criteria for multiparameter stochastic processes and some applications, Ann. Math. Statistics, 42, 1656-1670 (1971) · Zbl 0265.60011
[2] Billingsley, P., Convergence of probability measures (1968), New York: Wiley, New York · Zbl 0172.21201
[3] Davydov, Yu. A., Convergence of distributions generated by stationary stochastic processes, Theory Probab. Appl., 12, 691-696 (1968) · Zbl 0181.44101
[4] Deo, C. M., A note on empirical processes of strong-mixing sequences, Ann. Probab., 1, 870-875 (1973) · Zbl 0281.60034
[5] Ibragimov, I.; Linnik, Yu. V., Independent and stationary sequences of random variables (1971), Groningen: Wolters-Noordhoff Publishing, Groningen · Zbl 0219.60027
[6] Sen, P. K., A note on weak convergence of empirical processes for sequences of Φ-mixing random variables, Ann. Math. Statistics, 42, 2131-2133 (1971) · Zbl 0226.60008
[7] Sen, P. K., Weak convergence of multi-dimensional empirical processes for stationary Φ-mixing processes, Ann. Probab., 2, 147-154 (1974) · Zbl 0276.60030
[8] Yokoyama, R., Weak convergence of empirical processes for strong mixing sequences of random variables, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A., 12, No. 318, 36-39 (1973) · Zbl 0291.60020
[9] Yoshihara, K., Extensions of Billingsley’s theorems on weak convergence of empirical processes, Z. Wahrscheinlichkeitstheorie verw. Geb., 29, 87-92 (1974) · Zbl 0269.60035
[10] Yoshihara, K., Billingsley’s theorems on empirical processes of strong mixing sequences, Yokohama Math. J., 23, 1-7 (1975) · Zbl 0339.60030
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