28 Oct, 2017 The slide file was uploaded.

**タイトル**

Halting Probability $\Omega$

**種類**

A talk in Young gathering on mathematical founcations

**ダウンロード**

young

The theme of this wordpress changed to twenty seventeen.

]]>7 Oct, 2017 The slide file was uploaded.

**タイトル**

Face randomness by mathematics

**種類**

A talk in Mathpower

**ダウンロード**

mathpower_miyabe

15 Sep, 2017. The slide file was uploaded

**Title**

Solomonoff’s universal induction, or algorithmic probability

**Type**

Invited talk at SIG-AGI

**Download**

slide

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

**Title**

Turing degree

**Type**

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

**Download**

A resume in Japanese can be downloaded from the website.

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

Gave up for publication.

Rejected.

**Title**

Null-additivity in the theory of algorithmic randomness

**Type**

Full paper

**Journal**

**Abstract**

**download**

additive

22 Apr, 2016. The slide file was uploaded

**Title**

Berry’s paradox

**Type**

Freshman seminar at math department of Meiji University

**Download**

Slide in Japanese

22 Apr, 2016. The slide file was uploaded

**Title**

Random numbers

**Type**

A talk at a high school

**Download**

Slide (in Japanese)

24 Mar, 2016. The slide file was uploaded

**Title**

Can one compute a more random set uniformly?

**Type**

A talk at a meeting of Mathematical Society of Japan

**Download**

mathsoc