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

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:128

Article

Sato, Ryosuke¹  Miyabe, Kenshi²  Takemura, Akimichi³ 

[1] Univ Tokyo, Grad Sch Informat Sci & Technol, Tokyo, Japan

[2] Meiji Univ, Sch Sci & Technol, Tokyo, Japan

[3] Shiga Univ, Ctr Data Sci Educ & Res, Hikone, Shiga, Japan

关键词: Constant-proportion betting strategy;    Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm;    One-sided unbounded game;    Self-normalized processes;    Upper class;   

DOI  :  10.1016/j.spa.2017.07.014

来源: Elsevier

【 摘 要 】

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 Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm. (C) 2017 The Authors. Published by Elsevier B.V.

【 授权许可】

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