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The limiting distribution of the St. Petersburg game

Author: Ilan Vardi
Journal: Proc. Amer. Math. Soc. 123 (1995), 2875-2882
MSC: Primary 60F05
MathSciNet review: 1322939
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Abstract: The St. Petersburg game is a well-known example of a random variable which has infinite expectation. Csörgő and Dodunekova have recently shown that the accumulated winnings do not have a limiting distribution, but that if measurements are taken at a subsequence $ {b_n}$, then a limiting distribution exists exactly when the fractional parts of $ {\log _2}{b_n}$ approach a limit. In this paper the characteristic functions of these distributions are computed explicitly and found to be continuous, self-similar, nowhere differentiable functions.

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