Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit

István Berkes (), László Györfi () and Péter Kevei ()
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István Berkes: Graz University of Technology
László Györfi: Budapest University of Technology and Economics
Péter Kevei: Technische Universität München

Journal of Theoretical Probability, 2017, vol. 30, issue 3, 1104-1129

Abstract: Abstract We provide exact asymptotics for the tail probabilities $${\mathbb {P}}\{ S_{n,r} > x \}$$ P { S n , r > x } as $$x \rightarrow \infty $$ x → ∞ , for fixed n, where $$S_{n,r}$$ S n , r is the r-trimmed partial sum of i.i.d. St. Petersburg random variables. In particular, we prove that although the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also determine the exact tail behavior of the r-trimmed limits.

Keywords: St. Petersburg sum; Trimmed sum; Tail asymptotic; Semistable law; 60F05; 60E07 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10959-016-0677-5

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