Erdos-Feller-Kolmogorov-Petrowsky law of the iterated logarithm for self-normalized martingales: a game-theoretic approach

Abstract: 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.