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On Limit Theorems for Continued Fractions

Author

Listed:
  • Zbigniew S. Szewczak

    (Nicolaus Copernicus University)

Abstract

It is shown that for sums of functionals of digits in continued fraction expansions the Kolmogorov-Feller weak laws of large numbers and the Khinchine-Lévy-Feller-Raikov characterization of the domain of attraction of the normal law hold.

Suggested Citation

  • Zbigniew S. Szewczak, 2009. "On Limit Theorems for Continued Fractions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 239-255, March.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-007-0139-1
    DOI: 10.1007/s10959-007-0139-1
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    References listed on IDEAS

    as
    1. Szewczak, Zbigniew S., 2001. "Relative Stability for Strictly Stationary Sequences," Journal of Multivariate Analysis, Elsevier, vol. 78(2), pages 235-251, August.
    2. Jakubowski, Adam, 1993. "Minimal conditions in p-stable limit theorems," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 291-327, February.
    3. A. Gut, 2004. "An Extension of the Kolmogorov–Feller Weak Law of Large Numbers with an Application to the St. Petersburg Game," Journal of Theoretical Probability, Springer, vol. 17(3), pages 769-779, July.
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    Cited by:

    1. Alina Bazarova & István Berkes & Lajos Horváth, 2016. "On the Extremal Theory of Continued Fractions," Journal of Theoretical Probability, Springer, vol. 29(1), pages 248-266, March.

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