24 Feb, 2018 The slide file was uploaded.

**Title**

Continuity of limit computable functions at 1-generic points

**Type**

A talk in a seminar with Suzuki lab(in Japanese)

**Download**

tmu

24 Dect, 2017 The slide file was uploaded.

**Title**

A hierarchy of functions corresponding randomness hierarchy

**Type**

A talk in RIMS workshop “Proof theory and proving”

**Download**

rims

13 Dect, 2017 The slide file was uploaded.

**Title**

Computation at random points

**Type**

A talk in IPA Math 2017

**Download**

IPAmath

13 Dec, 2017 The slide file was uploaded.

**Title**

What is mathematics at all?

**Type**

A lecture in Meiji University Meiji High School at 6 Dec, 2017.

**Download**

math

28 Oct, 2017 The slide file was uploaded.

**Title**

Halting Probability $\Omega$

**Type**

A talk in Young gathering on mathematical founcations

**Download**

young

The theme of this wordpress changed to twenty seventeen.

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

**Title**

Face randomness by mathematics

**Type**

A talk in Mathpower

**Download**

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