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 framework and show that many classical results are still valid. © 2008 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Chernov, A., Shen, A., Vereshchagin, N., & Vovk, V. (2008). On-line probability, complexity and randomness. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5254 LNAI, pp. 138–153). https://doi.org/10.1007/978-3-540-87987-9_15
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