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Almost sure limit theorems for the St. Petersburg game

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  • Berkes, István
  • Csáki, Endre
  • Csörgo, Sándor

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.

Suggested Citation

  • Berkes, István & Csáki, Endre & Csörgo, Sándor, 1999. "Almost sure limit theorems for the St. Petersburg game," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 23-30, October.
    • Handle: RePEc:eee:stapro:v:45:y:1999:i:1:p:23-30
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    References listed on IDEAS

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    1. Fahrner, I. & Stadtmüller, U., 1998. "On almost sure max-limit theorems," Statistics & Probability Letters, Elsevier, vol. 37(3), pages 229-236, March.
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    Cited by:

    1. Nakata, Toshio, 2017. "A note on the asymptotics of the maxima for the St. Petersburg game," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 284-287.
    2. István Fazekas & Alexey Chuprunov, 2007. "An Almost Sure Functional Limit Theorem for the Domain of Geometric Partial Attraction of Semistable Laws," Journal of Theoretical Probability, Springer, vol. 20(2), pages 339-353, June.
    3. István Berkes & László Györfi & Péter Kevei, 2017. "Tail Probabilities of St. Petersburg Sums, Trimmed Sums, and Their Limit," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1104-1129, September.
    4. Zoltán Megyesi, 2002. "Domains of Geometric Partial Attraction of Max-Semistable Laws: Structure, Merge and Almost Sure Limit Theorems," Journal of Theoretical Probability, Springer, vol. 15(4), pages 973-1005, October.
    5. Berkes, István & Csáki, Endre, 2001. "A universal result in almost sure central limit theory," Stochastic Processes and their Applications, Elsevier, vol. 94(1), pages 105-134, July.
    6. Karjala, Melanie K. & Sherry, Erin E. & Dewhurst, Stephen M., 2004. "Criteria and indicators for sustainable forest planning: a framework for recording Aboriginal resource and social values," Forest Policy and Economics, Elsevier, vol. 6(2), pages 95-110, March.

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