Abstract
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.
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Chernov, A., Shen, A., Vereshchagin, N., Vovk, V. (2008). On-Line Probability, Complexity and Randomness. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds) Algorithmic Learning Theory. ALT 2008. Lecture Notes in Computer Science(), vol 5254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87987-9_15
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DOI: https://doi.org/10.1007/978-3-540-87987-9_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87986-2
Online ISBN: 978-3-540-87987-9
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