Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach

摘要

We prove an Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithmfor self-normalized martingales. Our proof is given in the framework of thegame-theoretic probability of Shafer and Vovk. As many other game-theoreticproofs, our proof is self-contained and explicit.