Algorithmic information theory and martingales

Details Algorithmic information theory and martingales Algorithmic information theory and martingales

2009-06-15

arxiv.org/abs/0906.2614v1

Mathematics

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Scientific paper

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.

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