Algorithmic information theory and martingales
History and Overview
2025-08-27 v2
Abstract
The notion of an individual random sequence goes back to von Mises. We describe the evolution of this notion, especially the use of martingales (suggested by Ville), and the development of algorithmic information theory in 1960s and 1970s (Solomonov, Kolmogorov, Martin-Lof, Levin, Chaitin, Schnorr and others). We conclude with some remarks about the use of the algorithmic information theory in the foundations of probability theory.
Cite
@article{arxiv.0906.2614,
title = {Algorithmic information theory and martingales},
author = {Laurent Bienvenu and Alexander Shen},
journal= {arXiv preprint arXiv:0906.2614},
year = {2025}
}
Comments
Corrected in 2025: Levin Leonid Anatolievich (not Alexandrovich, as it was by error)