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  • Autor
    • Berkes, István
    • Györfi, László
    • Kevei, Péter
  • TitelTail probabilities of St. Petersburg sums, trimmed sums, and their limit
  • Volltext
  • DOI10.1007/s10959-016-0677-5
  • Erschienen inJournal of Theoretical Probability
  • LicenceCC BY
  • ISSN1572-9230
  • ZugriffsrechteCC-BY
  • Download Statistik25
  • Peer ReviewNein
  • AbstractWe provide exact asymptotics for the tail probabilities \(\mathbb{P}\{S_n > x\}\) and \(\mathbb{P}\{S_n − X_n^∗ > x\}\) as \(x → ∞\), for fix n, where \(S_n\) and \(X_n^∗\) is the partial sum and partial maximum of i.i.d. St. Pe- tersburg random variables. We show that while the order of the tail of the sum \(S_n\) is \(x^{−1}\) , the order of the tail of the trimmed sum \(S_n − X_n^∗\) is \(x^{−2}\) . In particular, we prove that al- though the St. Petersburg distribution is only O-subexponential, the subexponential property almost holds. We also provide an infinite series representation of the distribution function of the limiting distribution of the trimmed sum, and analyze its tail behavior.