The Annals of Probability

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

Takeyuki Sasai, Kenshi Miyabe, and Akimichi Takemura

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We prove an Erdős–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. Like many other game-theoretic proofs, our proof is self-contained and explicit.

Article information

Ann. Probab., Volume 47, Number 2 (2019), 1136-1161.

Received: April 2015
Revised: December 2017
First available in Project Euclid: 26 February 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60G42: Martingales with discrete parameter

Bayesian strategy constant-proportion betting strategy lower class upper class self-normalized processes


Sasai, Takeyuki; Miyabe, Kenshi; Takemura, Akimichi. Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach. Ann. Probab. 47 (2019), no. 2, 1136--1161. doi:10.1214/18-AOP1281.

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