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

2017年8月8日　オンライン
2017年7月28日　SPA受理

タイトル
Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability
(with R. Sato and A. Takemura)

Stochastic Processes and their Applications
The page at SPA

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 selfnormalized
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.

ダウンロード
arXiv