Limit Theorems for the Petersburg Game

  • Sándor Csörgő
  • Rossitza Dodunekova
Part of the Progress in Probability book series (PRPR, volume 23)


We determine all possible subsequences \(\left\{ {n_k } \right\}_{k = 1}^\infty\)of the positive integers for which the suitably centered and normalized total gain S nk in n k Petersburg games has an asymptotic distribution as k → ∞, and identify the corresponding set of Hmiting distributions. We also solve all the companion problems for lightly, moderately, and heavily trimmed versions of the sum S nk and for the respective sums of extreme values in S nk .


Limit Theorem Asymptotic Distribution Total Gain Partial Attraction Divisible Distribution 
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Copyright information

© Birkhäuser Boston 1991

Authors and Affiliations

  • Sándor Csörgő
    • 1
  • Rossitza Dodunekova
    • 2
  1. 1.Department of StatisticsThe University of MichiganAnn ArborUSA
  2. 2.Department of Probability and StatisticsUniversity of SofiaSofiaBulgaria

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