Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach

履歴
2018年5月4日 AOP受理

タイトル
Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach
(with T. Sasai and A. Takemura)

種類
正論文

国際会議と雑誌
Annals of Probability,
Annals of Probability, Vol. 47, No. 2, 1136-1161, March 2019.

Abstract
We prove an Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales. Our proof is given in the framework of the game-theoretic probability of Shafer and Vovk. As many other game-theoretic proofs, our proof is self-contained and explicit.

ダウンロード
arXiv

Muchnik degrees and Medvedev degrees of the randomness notions

履歴
2018年9月 受理
2018年3月11日 投稿

タイトル
Muchnik degrees and Medvedev degrees of the randomness notions

種類
研究論文

国際会議と雑誌
ALC2015とALC2017の共同議事録
World Scientificから出版予定

Proceedings of the 14th and 15th Asian Logic Conferences, pp. 108-128 (2019) January

Abstract
The main theme of this paper is computational power when a machine is allowed to access random sets.
The computability depends on the randomness notions and we compare them by Muchnik and Medvedev degrees.
The central question is whether, given an random oracle, one can compute a more random set.
The main result is that, for each Turing functional,
there exists a Schnorr random set whose output is not computably random.

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Muchnikdegrees