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

DOI10.1214/18-AOP1281zbMATH Open1466.60086arXiv1504.06398OpenAlexW2962757666MaRDI QIDQ2414153

Akimichi Takemura, Kenshi Miyabe, Takeyuki Sasai

Publication date: 10 May 2019

Published in: The Annals of Probability (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1504.06398

zbMATH Keywords

Bayesian strategyself-normalized processeslower classupper classconstant-proportion betting strategy

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42)

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