Kenshi Miyabe

履歴
2017年8月8日　オンライン
2017年7月28日　SPA受理

タイトル
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)

種類
正論文

国際会議と雑誌
Stochastic Processes and their Applications
Volume 128, Issue 5, May 2018, Pages 1466-1484
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.

ダウンロード
arXiv

履歴
2018年3月19日 オンライン
2018年3月5日　JLA受理

タイトル
Randomness and Solovay degrees
(with A. Nies and F. Stephan)

種類
正論文

国際会議と雑誌
Journal of Logic and Analysis, Vol 10, pp.1–13, 2018.
Open access

Abstract
We consider the behaviour of Schnorr randomness, a randomness notion weaker than Martin-L\”of’s, for left-r.e. reals under Solovay reducibility. Contrasting with results on Martin-L\”of-randomenss, we show that Schnorr randomness is not upward closed in the Solovay degrees. Next, some left-r.e. Schnorr random $\alpha$ is the sum of two left-r.e. reals that are far from random. We also show that the left-r.e. reals of effective dimension $>r$, for some rational $r$, form a filter in the Solovay degrees.

ダウンロード

coromandel_JLA_final

履歴
2018年3月11日提出

タイトル
計算可能測度論

種類
総説論文

ジャーナル
数理解析研究所講究録
RIMS共同研究(公開型)証明論と証明活動
2017年12月25日〜27日

ダウンロード
rims