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Literature Cited
S. A. Utev, “Sums of random variables with ϕ-mixing,” Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,13, 78–100 (1989).
S. A. Utev, “Central limit theorem for dependent random variables,”. in: Proc. Fifth Vilnius Conference on Probab. Theory, Vol. 2, Vilnius (1990), pp. 519–528.
R. C. Bradley, “Asymptotic normality of some kernel-type estimators of probability density,” Statistics Probab. Lett.,1, No. 6, 295–300 (1983).
S. A. Utev, “Central limit theorem for schemes of series of random variables with ϕ-mixing,” Teor. Veroyatn. Primen.,35, No. 1, 110–117 (1990).
A. Jakubowski and M. Kobus, “α-stable limit theorems for sums of dependent random vectors,” J. Multiv. Anal.,29, No. 2, 219–251 (1989).
A. G. Grin', “Domains of attraction for sequences with mixing,” Sib. Mat. Zh.,31, No. 1, 53–63 (1990).
M. Peligrad, “The r-quick version of the strong law for stationary Φ-mixing sequences,” Almost Everywhere Convergence (1989), pp. 335–348.
H. Berbee, “Random walks with stationary increments and renewal theory,” Mathematical Centre, Amsterdam (1979).
I. Berkes and W. Philipp, “Approximation theorems for independent and weakly dependent random vectors,” Ann. Probab.,7, No. 1, 29–54 (1979).
I. A. Ibragimov, “Remark on the central limit theorem for dependent random variables,” Teor. Veroyatn. Primen.,20, No. 1, 134–140 (1975).
J. Hoffman-Jørgensen, “Sums of independent Banach space valued random variables,” Stud. Math.,52, No. 2, 159–186 (1974).
J. Hoffman-Jørgensen and G. Pisier, “The law of large numbers and the central limit theorem in Banach spaces,” Ann. Probab.,4, No. 4, 587–599 (1976).
R. Lapinskas, “Limit theorems for weakly dependent random variables in some Banach spaces,” Lit. Mat. Sb.,24, No. 1, 111–120 (1984).
J. Samur, “Convergence of sums of mixing triangular arrays of random vectors with stationary rows,” Ann. Probab.,12, No. 2, 390–426 (1984).
J. Kuelbs and W. Philipp, “Almost sure invariance principles for partial sums of mixing B-valued random variables,” Ann. Probab.,8, No. 6, 1003–1036 (1980).
V. Yu. Bentkus, “Asymptotics of moments in the central limit theorem in Banach spaces,” Lit. Mat. Sb.,24, No. 2, 49–64 (1984).
A. D. Venttsel', “Improvement of the functional central limit theorem for stationary processes,” Teor. Veroyatn., Primen.,35, No. 3, 451–464 (1989).
T. M. Zuparov, “Estimates of the rate of convergence in the central limit theorem for absolutely regular random variables with values in some Banach spaces,” Dokl. Akad. Nauk SSSR,272, No. 5, 1042–1045 (1983).
S. A. Utev, “Inequalities for sums of weakly dependent random variables and estimates of the rate of convergence in the invariance principle,” Tr. Inst. Mat. Sib. Otd. Akad. Nauk SSSR,3, 50–76 (1984).
J. Hüsler, “Extreme values and rare events of nonstationary random sequences,” in: Dependence in Probability and Statistics, Birkhäuser (1986), pp. 439–456.
R. M. Loynes, “Extreme values in uniformly mixing stationary stochastic processes,” Ann. Math. Stat.,36, No. 3, 993–999 (1965).
V. N. Hudson, H. G. Tucker, and J. A. Veeh, “Limit distribution of sums of m-dependent Bernoulli random variables,” Probab. Theory Related Fields,82, No. 1, 9–17 (1989).
H. A. Krieger, “A new look at Bergström's theorem on convergence in distribution for sums of dependent random variables,” Isr. J. Math.,47, No. 1, 32–64 (1984).
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Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 4, pp. 165–183, July–August, 1991.
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Utev, S.A. Sums of weakly dependent random variables. Sib Math J 32, 675–690 (1991). https://doi.org/10.1007/BF00972986
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DOI: https://doi.org/10.1007/BF00972986