3 citations · 5 across the 7 of their papers we have counts for
8 papers
Ball codes: A coding characterization of Hausdorff and packing dimensions
Kenshi Miyabe
We prove a purely classical, coding-theoretic characterization of Hausdorff and packing dimensions in \(\mathbb R^n\). A \emph{ball code} assigns names to closed balls of \(\mathbb…
Solovay reduction and continuity
Masahiro Kumabe, Kenshi Miyabe, Yuki Mizusawa +1
The objective of this study is a better understanding of the relationships between reduction and continuity. Solovay reduction is a variation of Turing reduction based on the dista…
Relation between the rate of convergence of strong law of large numbers and the rate of concentration of Bayesian prior in game-theoretic probability
Ryosuke Sato, Kenshi Miyabe, Akimichi Takemura
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 p…
Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach
Takeyuki Sasai, Kenshi Miyabe, Akimichi Takemura
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 o…
Using almost-everywhere theorems from analysis to study randomness
Kenshi Miyabe, André Nies, Jing Zhang
We study algorithmic randomness notions via effective versions of almost-everywhere theorems from analysis and ergodic theory. The effectivization is in terms of objects described…
Derandomization in Game-theoretic Probability
Kenshi Miyabe, Akimichi Takemura
We give a general method for constructing a deterministic strategy of Reality from a randomized strategy in game-theoretic probability. The construction can be seen as derandomizat…
Van Lambalgen's Theorem for uniformly relative Schnorr and computable randomness
Kenshi Miyabe, Jason Rute
We correct Miyabe's proof of van Lambalgen's Theorem for truth-table Schnorr randomness (which we will call uniformly relative Schnorr randomness). An immediate corollary is one di…
Convergence of random series and the rate of convergence of the strong law of large numbers in game-theoretic probability
Kenshi Miyabe, Akimichi Takemura
We give a unified treatment of the convergence of random series and the rate of convergence of strong law of large numbers in the framework of game-theoretic probability of Shafer…