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The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models

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  • Giuliano-Antonini, R.
  • Weber, M.

Abstract

We prove a weighted Almost Sure Limit Theorem in the setting of random iterative models. This theorem generalizes previous results obtained for sequences of normalized partial sums and some other classes of random sequences.

Suggested Citation

  • Giuliano-Antonini, R. & Weber, M., 2008. "The theta-dependence coefficient and an Almost Sure Limit Theorem for random iterative models," Statistics & Probability Letters, Elsevier, vol. 78(5), pages 564-575, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:5:p:564-575
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    References listed on IDEAS

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    1. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
    2. Doukhan, Paul & Louhichi, Sana, 1999. "A new weak dependence condition and applications to moment inequalities," Stochastic Processes and their Applications, Elsevier, vol. 84(2), pages 313-342, December.
    3. Lacey, Michael T. & Philipp, Walter, 1990. "A note on the almost sure central limit theorem," Statistics & Probability Letters, Elsevier, vol. 9(3), pages 201-205, March.
    4. Dedecker, Jérôme & Doukhan, Paul, 2003. "A new covariance inequality and applications," Stochastic Processes and their Applications, Elsevier, vol. 106(1), pages 63-80, July.
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    Cited by:

    1. Giuliano, Rita & Szewczak, Zbigniew S., 2014. "A general correlation inequality and the Almost Sure Local Limit Theorem for random sequences in the domain of attraction of a stable law," Stochastic Processes and their Applications, Elsevier, vol. 124(4), pages 1612-1626.

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