Almost sure limit theorems for the St. Petersburg game

István Berkes, E. Csáki, Sándor Csörgo

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

We show that the accumulated gain Sn and the maximal gain Mn in n St. Petersburg games satisfy almost sure limit theorems with nondegenerate limits, even though ordinary asymptotic distributions do not exist for Sn and Mn with any numerical centering and norming sequences.

Original languageEnglish
Pages (from-to)23-30
Number of pages8
JournalStatistics and Probability Letters
Volume45
Issue number1
Publication statusPublished - Oct 15 1999

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Almost Sure Limit Theorem
Game
Asymptotic distribution
Limit theorems

Keywords

  • Almost sure limit theorems
  • Asymptotic distributions
  • Primary 60F15
  • Secondary 60F05
  • St. Petersburg game

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Statistics and Probability

Cite this

Almost sure limit theorems for the St. Petersburg game. / Berkes, István; Csáki, E.; Csörgo, Sándor.

In: Statistics and Probability Letters, Vol. 45, No. 1, 15.10.1999, p. 23-30.

Research output: Contribution to journalArticle

Berkes, István ; Csáki, E. ; Csörgo, Sándor. / Almost sure limit theorems for the St. Petersburg game. In: Statistics and Probability Letters. 1999 ; Vol. 45, No. 1. pp. 23-30.
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