### Solomonoff’s universal induction, or algorithmic probability

News
15 Sep, 2017. The slide file was uploaded

Title
Solomonoff’s universal induction, or algorithmic probability

Type
Invited talk at SIG-AGI

slide

### Turing degree

News
5-7 Aug, 2017. Summer School of mathematical foundations

Title
Turing degree

Type
A lecture at summer school of mathematical foundations (in Japanese)

A resume in Japanese can be downloaded from the website.

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

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.

arXiv

### Null-additivity in the theory of algorithmic randomness

News
Gave up for publication.
Rejected.

Title
Null-additivity in the theory of algorithmic randomness

Type
Full paper

Journal

Abstract