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Strong laws of large numbers for intermediately trimmed Birkhoff sums of observables with infinite mean

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  • Kesseböhmer, Marc
  • Schindler, Tanja

Abstract

We consider dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable. For such systems we generalize strong laws of large numbers for intermediately trimmed sums only known for independent random variables. The results split up in trimming statements for general distribution functions and for regularly varying tail distributions. In both cases the trimming rate can be chosen in the same or almost the same way as in the i.i.d. case. As an example we show that piecewise expanding interval maps fulfill the necessary conditions for our limit laws. As a side result we obtain strong laws of large numbers for truncated Birkhoff sums.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:10:p:4163-4207
    DOI: 10.1016/j.spa.2018.11.015
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    References listed on IDEAS

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    1. 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.
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