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March 2019 Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach
Takeyuki Sasai, Kenshi Miyabe, Akimichi Takemura
Ann. Probab. 47(2): 1136-1161 (March 2019). DOI: 10.1214/18-AOP1281

Abstract

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.

Citation

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Takeyuki Sasai. Kenshi Miyabe. Akimichi Takemura. "Erdős–Feller–Kolmogorov–Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach." Ann. Probab. 47 (2) 1136 - 1161, March 2019. https://doi.org/10.1214/18-AOP1281

Information

Received: 1 April 2015; Revised: 1 December 2017; Published: March 2019
First available in Project Euclid: 26 February 2019

zbMATH: 07053566
MathSciNet: MR3916944
Digital Object Identifier: 10.1214/18-AOP1281

Subjects:
Primary: 60G42

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 2 • March 2019
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