Algorithmic information theory and martingales
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arXiv
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| Format: | Preprint |
| Published: |
2009
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| _version_ | 1866915462240010240 |
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| author | Bienvenu, Laurent Shen, Alexander |
| author_facet | Bienvenu, Laurent Shen, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0906_2614 |
| institution | arXiv |
| publishDate | 2009 |
| record_format | arxiv |
| spellingShingle | Algorithmic information theory and martingales Bienvenu, Laurent Shen, Alexander History and Overview 68Q30, 60A99 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. |
| title | Algorithmic information theory and martingales |
| topic | History and Overview 68Q30, 60A99 |
| url | https://arxiv.org/abs/0906.2614 |