18 Mar, 2019 The slide file was uploaded.
Coherence between reducibility and randomness notions
A talk in Mathematical Society of Japan
18 Mar, 2019@TITech
May 4, 2018. Accepted by AOP
Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach
(with T. Sasai and A. Takemura)
Annals of Probability,
Annals of Probability, Vol. 47, No. 2, 1136-1161, March 2019.
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.
Sep 2018, accepted
11 Mar 2018, submitted to a Journal
Muchnik degrees and Medvedev degrees of the randomness notions
The joint post-proceedings for ALC2015 and ALC2017 published via World Scientific
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.