The limiting distribution of the St. Petersburg game
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- by Ilan Vardi PDF
- Proc. Amer. Math. Soc. 123 (1995), 2875-2882 Request permission
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.References
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Additional Information
- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2875-2882
- MSC: Primary 60F05
- DOI: https://doi.org/10.1090/S0002-9939-1995-1322939-3
- MathSciNet review: 1322939