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

Marc Kesseböhmer and Tanja Schindler

Stochastic Processes and their Applications, 2019, vol. 129, issue 10, 4163-4207

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.

Keywords: Almost sure convergence theorems; Trimmed sum process; Transfer operator; Spectral method; Piecewise expanding interval map; Strong law of large numbers (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1016/j.spa.2018.11.015

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