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Trimmed sums for non-negative, mixing stationary processes

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  • Aaronson, Jon
  • Nakada, Hitoshi

Abstract

We consider the effect of "trimming" ergodic sums of their maximal values on the strong law of large numbers for non-negative, non-integrable, mixing stationary processes. The results obtained are used to show the failure of the strong law of large numbers for modified continued fraction coefficients, and to study the "cusp visits" of a certain interval map.

Suggested Citation

  • Aaronson, Jon & Nakada, Hitoshi, 2003. "Trimmed sums for non-negative, mixing stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 104(2), pages 173-192, April.
    • Handle: RePEc:eee:spapps:v:104:y:2003:i:2:p:173-192
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    Cited by:

    1. Takahasi, Hiroki, 2022. "Large deviation principle for the backward continued fraction expansion," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 153-172.
    2. Kesseböhmer, Marc & Schindler, Tanja, 2019. "Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4163-4207.
    3. Marc Kesseböhmer & Tanja Schindler, 2019. "Strong Laws of Large Numbers for Intermediately Trimmed Sums of i.i.d. Random Variables with Infinite Mean," Journal of Theoretical Probability, Springer, vol. 32(2), pages 702-720, June.

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