Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability

Ryosuke Sato, Kenshi Miyabe and Akimichi Takemura

Stochastic Processes and their Applications, 2018, vol. 128, issue 5, 1466-1484

Abstract: We study the behavior of the capital process of a continuous Bayesian mixture of fixed proportion betting strategies in the one-sided unbounded forecasting game in game-theoretic probability. We establish the relation between the rate of convergence of the strong law of large numbers in the self-normalized form and the rate of divergence to infinity of the prior density around the origin. In particular we present prior densities ensuring the validity of Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm.

Keywords: Constant-proportion betting strategy; Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm; One-sided unbounded game; Self-normalized processes; Upper class (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:128:y:2018:i:5:p:1466-1484

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DOI: 10.1016/j.spa.2017.07.014

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