23 citations · 23 across the 1 of their papers we have counts for
3 papers
math.PR2006★ 23 cited
Game-theoretic versions of strong law of large numbers for unbounded variables
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality…
math.ST2005
Capital process and optimality properties of a Bayesian Skeptic in coin-tossing games
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic…
math.PR2005
On a simple strategy weakly forcing the strong law of large numbers in the bounded forecasting game
Masayuki Kumon, Akimichi Takemura
In the framework of the game-theoretic probability of Shafer and Vovk (2001) it is of basic importance to construct an explicit strategy weakly forcing the strong law of large numb…