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
Volume 128, Issue 5, May 2018, Pages 1466-1484
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.
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arXiv