Kenshi Miyabe

News
16 May 2013, Submitted to a Journal

Title
Uniform Kurtz randomness
(with Takayuki Kihara)

Type
Fullpaper

Journal
Submitted.

Abstract
We propose studying uniform Kurtz randomness, which is the uni- form relativization of Kurtz randomness. This notion has more natural properties than the usual relativization. For instance, van Lambalgen’s theorem holds for uniform Kurtz randomness while not for (the usual relativization of) Kurtz randomness. Another advantage is that lowness for uniform Kurtz randomness has many characterizations, such as those via complexity, martingales, Kurtz tt-traceability, and Kurtz dimensional measure.

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preprint

News
19 Mar 2013, Accepted
25 Aug 2012, Submitted to a Journal

Title
The law of the iterated logarithm in game-theoretic probability with quadratic and stronger hedges
(with Akimichi Takemura)

Type
Fullpaper

Journal
Stochastic Processes and their Applications, 123, 3132-3152, 2013.

Abstract
We prove both the validity and the sharpness of the law of the iter- ated logarithm in game-theoretic probability with quadratic and stronger hedges.

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arXiv
preprint

News
27 Mar 2013, accepted
19 Sep 2012, submitted

Title
L1-computability, layerwise computability and Solovay reducibility

Type
Full paper

Journal
To appear in Computability

Abstract
We propose a hierarchy of classes of functions that corresponds to the hierarchy of randomness notions. Each class of functions converges at the corresponding random points. We give various characterizations of the classes, that is, characterizations via integral tests, L1-computability and layerwise computability. Furthermore, the relation among these classes is formulated using Solovay reducibility for lower semicomputable functions.

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preprint

News
23 Mar 2013, Submitted

Title
Schnorr triviality and its equivalent notions

Type
Full paper

Journal
Submitted

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preprint

News
15 Mar 2013, Submitted

Title
Computation with advice of degree of randomness

Type
Survey

Journal
RIMS Kokyuroku
28 – 30 Jan 2013

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preprint