An exponential inequality and the convergence rate of the strong law of large numbers in the unbounded forecasting game

作者：Takazawa Shin ichiro^*

来源：Stochastics: An International Journal of Probability and Stochastic Processes , 2011, 83(2): 117-125.

DOI：10.1080/17442508.2010.538692

• exponential inequality
• game-theoretic probability
• strong law of large numbers
• convergence rate

In this paper, we study a large deviation inequality in the framework of the game-theoretic probability of Shafer and Vovk (Probability and Finance: It's only a game! Wiley, 2001). First, we propose an exponential inequality in the unbounded forecasting game. In addition, by using the exponential inequality, we prove that in the unbounded forecasting game, under some conditions, Skeptic can force the strong law of large numbers with the convergence rate of [image omitted].

• 出版日期2011