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

Authors
Sasai, Takeyuki Takemura, Akimichi Miyabe, Kenshi
Citation
Sasai, Takeyuki et al., Erd.s.Feller.Kolmogorov.Petrowsky law of the iterated logarithm for self-normalized martingales: A game-theoretic approach., Annals of probability (Online) , 47(2), 2019, pp. 1136-1161
Journal title
Annals of probability (Online) → ACNP
ISSN journal
2168894X
Volume
47
Issue
2
Year of publication
2019
Pages
1136 - 1161
Database
ACNP
SICI code
Abstract
We prove an Erd.s.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.