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Extreme-trimmed St. Petersburg games

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  • Gut, Allan
  • Martin-Löf, Anders

Abstract

Let Sn, n≥1, describe the successive sums of the payoffs in the classical St. Petersburg game. Feller’s famous weak law, Feller (1945), states that Snnlog2n→p1 as n→∞. However, almost sure convergence fails, more precisely, lim supn→∞Snnlog2n=+∞ a.s. and lim infn→∞Snnlog2n=1 a.s. as n→∞. Csörgő and Simons (1996) have shown that almost sure convergence holds for trimmed sums, that is, for Sn−max1≤k≤nXk and, moreover, that this remains true if the sums are trimmed by an arbitrary fixed number of maximal sums. A predecessor of the present paper was devoted to sums trimmed by the random number of maximal summands. The present paper concerns analogs for the random number of summands equal to the minimum, as well as analogs for joint trimmings.

Suggested Citation

  • Gut, Allan & Martin-Löf, Anders, 2015. "Extreme-trimmed St. Petersburg games," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 341-345.
    • Handle: RePEc:eee:stapro:v:96:y:2015:i:c:p:341-345
    DOI: 10.1016/j.spl.2014.09.006
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    References listed on IDEAS

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    1. Csörgo, Sándor & Simons, Gordon, 1996. "A strong law of large numbers for trimmed sums, with applications to generalized St. Petersburg games," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 65-73, January.
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