### Abstract

Original language | English |
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Title of host publication | 19th International Conference, ALT 2008 |

Place of Publication | Berlin |

Pages | 138-153 |

Number of pages | 16 |

Volume | 5254 |

DOIs | |

Publication status | Published - 31 Dec 2008 |

Event | 19th International Conference, ALT 2008 - Budapest, Hungary, October 13-16, 2008 Duration: 31 Dec 2008 → … |

### Publication series

Name | Lecture Notes in Computer Science |
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### Conference

Conference | 19th International Conference, ALT 2008 |
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Period | 31/12/08 → … |

### Fingerprint

### Bibliographical note

© Springer-Verlag Berlin Heidelberg 2008### Cite this

*19th International Conference, ALT 2008*(Vol. 5254, pp. 138-153). (Lecture Notes in Computer Science). Berlin. https://doi.org/10.1007/978-3-540-87987-9_15

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*19th International Conference, ALT 2008.*vol. 5254, Lecture Notes in Computer Science, Berlin, pp. 138-153, 19th International Conference, ALT 2008, 31/12/08. https://doi.org/10.1007/978-3-540-87987-9_15

**On-Line Probability, Complexity and Randomness.** / Chernov, Alexey; Shen, Alexander; Vereshchagin, Nikolai; Vovk, Vladimir.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › Research › peer-review

TY - GEN

T1 - On-Line Probability, Complexity and Randomness

AU - Chernov, Alexey

AU - Shen, Alexander

AU - Vereshchagin, Nikolai

AU - Vovk, Vladimir

N1 - © Springer-Verlag Berlin Heidelberg 2008

PY - 2008/12/31

Y1 - 2008/12/31

N2 - Classical probability theory considers probability distributions that assign probabilities to all events (at least in the finite case). However, there are natural situations where only part of the process is controlled by some probability distribution while for the other part we know only the set of possibilities without any probabilities assigned. We adapt the notions of algorithmic information theory (complexity, algorithmic randomness, martingales, a priori probability) to this frame work and show that many classical results are still valid.

AB - Classical probability theory considers probability distributions that assign probabilities to all events (at least in the finite case). However, there are natural situations where only part of the process is controlled by some probability distribution while for the other part we know only the set of possibilities without any probabilities assigned. We adapt the notions of algorithmic information theory (complexity, algorithmic randomness, martingales, a priori probability) to this frame work and show that many classical results are still valid.

U2 - 10.1007/978-3-540-87987-9_15

DO - 10.1007/978-3-540-87987-9_15

M3 - Conference contribution with ISSN or ISBN

SN - 9783540879862

VL - 5254

T3 - Lecture Notes in Computer Science

SP - 138

EP - 153

BT - 19th International Conference, ALT 2008

CY - Berlin

ER -