Implications of contrarian and one-sided strategies for the fair-coin game

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Implications of contrarian and one-sided strategies for the fair-coin game

We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [8]. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n−1/2). This is achieved by a very simple co...

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MATHEMATICAL ENGINEERING TECHNICAL REPORTS Implications of contrarian and one-sided strategies for the fair-coin game

We derive some results on contrarian and one-sided strategies by Skeptic for the fair-coin game in the framework of the game-theoretic probability of Shafer and Vovk [8]. In particular, concerning the rate of convergence of the strong law of large numbers (SLLN), we prove that Skeptic can force that the convergence has to be slower than or equal to O(n−1/2). This is achieved by a very simple co...

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ژورنال

عنوان ژورنال: Stochastic Processes and their Applications

سال: 2008

ISSN: 0304-4149

DOI: 10.1016/j.spa.2007.11.007