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On-Line Probability, Complexity and Randomness

  • Alexey Chernov
  • Alexander Shen
  • Nikolai Vereshchagin
  • Vladimir Vovk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5254)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Alexey Chernov
    • 1
  • Alexander Shen
    • 2
  • Nikolai Vereshchagin
    • 3
  • Vladimir Vovk
    • 1
  1. 1.Royal HollowayUniversity of LondonEghamUK
  2. 2.Marseille and Institute of Information Transmission ProblemsLIF (Université Aix-Marseille & CNRS)Moscow
  3. 3.Moscow State University 

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