Siberian Mathematical Journal

, Volume 25, Issue 1, pp 144–148 | Cite as

Law of the iterated logarithm for ϕ-mixing random variables

  • S. A. Utev


Iterate Logarithm 
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Literature Cited

  1. 1.
    C. C. Heyde and D. I. Scott, “Invariance principles for the law of the iterated logarithm, for martingales and processes with stationary increments,” Ann. Prob.,1, No. 3, 428–437 (1973).Google Scholar
  2. 2.
    W. Philipp, “The law of the iterated logarithm for mixing stochastic processes,” Ann. Math. Statist.,40, No. 6, 1985–1991 (1969).Google Scholar
  3. 3.
    W. Philipp and W. Stout, “Almost-sure invariance principles for partial sums of weakly dependent random variables,” Am. Math. Soc. Met.,2, No. 161 (1975).Google Scholar
  4. 4.
    A. Berkes and W. Philipp, “Approximation theorems for independent and weakly dependent random vectors,” Ann. Prob.,7, No. 1, 29–54 (1979).Google Scholar
  5. 5.
    C. C. Heyde, “Some properties of metrics on a study on convergence to normality,” Z. Wahrscheinlichkeitstheorie Verw. Geb.,11, No. 3, 181–192 (1969).Google Scholar
  6. 6.
    V. V. Petrov, Sums of Independent Random Variables, Springer-Verlag (1975).Google Scholar
  7. 7.
    S. A. Utev, “Some inequlities for weakly dependent random variables,” in: Third Vilnius Conference on Probability Theory and Mathematical Statistics. Contents of Dissertations, Vol. 2 (1981), pp. 204–205.Google Scholar
  8. 8.
    H. Cohn, “On a class of dependent random variables,” Rev. Roum. Pures Pures Appl.,10, No. 10, 1593–1606 (1965).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • S. A. Utev

There are no affiliations available

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