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  • 1 Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland
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Abstract

We consider the classical Kolmogorov condition for strong law of large numbers for sequences of dependent random variables; the so-called ϕ-mixing and Rademacher–Menchoff condition for ρ-mixing sequences.

  • [1] Bradley, R. 2001 A stationary rho-mixing Markov chain which is not “interlaced” rho-mixing J. Theoret. Probab. 14 717727 .

  • [2] Chen, P., Hu, T. C., Volodin, A. 2009 Limit behaviour of moving average processes under φ-mixing assumption Statist. Probab. Lett. 79 105111 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [3] Fazekas, I., Klesov, O. 2000 A general approach to the strong laws of large numbers Teor. Verojatnost. i Primenen. 45 569583.

  • [4] Ibragimov, I. A. 1962 Some limit theorems for stationary processes Theory Probab. Appl. 7 349382 .

  • [5] Iosifescu, M., Theodorescu, R. 1969 Random Processes and Learning Springer-Verlag Berlin – Heidelberg – New York.

  • [6] Kiesel, R. 1997 Strong laws and summability for sequences of φ-mixing random variables in Banach spaces Elect. Com. in Probab. 2 2241.

    • Search Google Scholar
    • Export Citation
  • [7] Kiesel, R. 1998 Summability and strong laws for φ-mixing random variables J. Theor. Probab. 11 209224 .

  • [8] Kolmogorov, A. N., Rozanov, H. 1960 On strong mixing for stationary Gaussian processes Theory Probab. Appl. 5 204208 .

  • [9] Liang, H. 1999 A note of convergence rates for sums of ρ-mixing sequences Ac. Math. App. Sinica 15 172177 .

  • [10] Peligrad, M. 1987 On the central limit theorem for ρ-mixing sequences of random variables Ann. Probab. 15 13871394 .

  • [11] Peligrad, M. 1989 The r-quick version of the strong law for stationary φ-mixing sequences Proc. Internat. Conf. on Almost Everywere Convergence in Probab. and Statist Academic Press New York 335348.

    • Search Google Scholar
    • Export Citation
  • [12] Peligrad, M., Shao, Q. M. 1995 Estimation of variance for ρ-mixing sequences J. Multivariate Anal. 52 140157 .

  • [13] Peligrad, M., Shao, Q. M. 1996 A note on estimation of the variance of partial sums for ρ-mixing random variables Statist. Probab. Lett. 28 141145 .

    • Crossref
    • Search Google Scholar
    • Export Citation
  • [14] Rozanov, Y. A., Volkonski, V. A. 1959 Some limit theorems for random function Theory Probab. 4 186207.

  • [15] Shao, Q. M. 1995 Maximal inequalities for partial sums of ρ-mixing sequences Ann. Probab. 23 948965 .

  • [16] Stout, W. 1974 Almost Sure Convergence Academic Press New York.

  • [17] Tuyen, D. Q. 1999 A strong law for mixing random variables Periodica Math. Hung. 38 131136 .

  • [18] Utev, S. A. 1991 Sums of random variables with φ-mixing Siberian Adv. Math. 1 124155.

  • [19] Zhang, L. 1996 Complete convergence of moving average processes under dependence assumptions Statist. Probab. Lett. 30 165170 .

  • [20] Zhengyan, L., Chuanrong, L. 1996 Limit Theory for Mixing Dependent Random Variables Kluver Academic Publishers.

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Acta Mathematica Hungarica
Language English
Size B5
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1950
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ISSN 0236-5294 (Print)
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