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

Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Theoretical Probability Springer Journals

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

, Volume 30 (3) – Mar 15, 2016
26 pages

/lp/springer_journal/tail-probabilities-of-st-petersburg-sums-trimmed-sums-and-their-limit-hCxP4n0YqE
Publisher
Springer US
Subject
Mathematics; Probability Theory and Stochastic Processes; Statistics, general
ISSN
0894-9840
eISSN
1572-9230
D.O.I.
10.1007/s10959-016-0677-5
Publisher site
See Article on Publisher Site

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.

Journal

Journal of Theoretical ProbabilitySpringer Journals

Published: Mar 15, 2016

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