**News**

8 Aug, 2017. Online

28 July 2017. accepted by SPA

**Title**

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)

**Type**

Full paper

**Journal**

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.

**download**

arXiv