Author
Tanja Schindler
Bio: Tanja Schindler is an academic researcher from Australian National University. The author has contributed to research in topics: Law of large numbers & Random variable. The author has an hindex of 6, co-authored 19 publications receiving 55 citations.
Papers
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TL;DR: In this paper, the authors considered dynamical systems on a finite measure space fulfilling a spectral gap property and Birkhoff sums of a non-negative, non-integrable observable.
13 citations
TL;DR: The classic Thue-Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval as mentioned in this paper, and many aspects of this measure have been studied in the past, including various scaling properties and a partly heuristic multifractal analysis.
Abstract: The classic Thue–Morse measure is a paradigmatic example of a purely singular continuous probability measure on the unit interval. Since it has a representation as an infinite Riesz product, many aspects of this measure have been studied in the past, including various scaling properties and a partly heuristic multifractal analysis. Some of the difficulties emerge from the appearance of an unbounded potential in the thermodynamic formalism. It is the purpose of this article to review and prove some of the observations that were previously established via numerical or scaling arguments.
11 citations
TL;DR: In this article, it was shown that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds.
Abstract: We show that for every sequence of nonnegative i.i.d. random variables with infinite mean there exists a proper moderate trimming such that for the trimmed sum process a non-trivial strong law of large numbers holds. We provide an explicit procedure to find a moderate trimming sequence even if the underlying distribution function has a complicated structure, e.g., has no regularly varying tail distribution.
9 citations
TL;DR: In this paper, the authors consider moderately trimmed sums of non-negative i.i.d. random variables and show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds.
Abstract: We consider moderately trimmed sums of non-negative i.i.d. random variables. We show that for every distribution function there exists a proper moderate trimming such that for the trimmed sum a non-trivial strong law of large numbers holds. In case that the distribution function has regularly varying tails we give necessary and sufficient conditions on the trimming for a strong law of large numbers to hold.
7 citations
TL;DR: In this paper, strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type were proved for large numbers over sub-shifts.
Abstract: We prove strong laws of large numbers under intermediate trimming for Birkhoff sums over subshifts of finite type. This gives another application of a previous trimming result only proven for inter...
7 citations
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