On-Line Probability, Complexity and Randomness
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.
Unable to display preview. Download preview PDF.
- 1.Gács, P.: Lecture notes on descriptional complexity and randomness, http://www.cs.bu.edu/faculty/gacs/papers/ait-notes.pdf
- 4.Muchnik An, A., Chernov, A., Shen, A.: Algorithmic randomness and splitting of supermartingales, arxiv.org:0807.3156Google Scholar
- 5.Shen, A.: Algorithmic information theory and Kolmogorov complexity, Technical Report 2000-034. Uppsala Universitet publication, http://www.it.uu.se/research/publications/reports/2000-034
- 8.Vovk, V., Shen, A.: Prequential randomness. In: Freund, Y., Györfi, L., Turán, G., Zeugmann, T. (eds.) ALT 2008. LNCS(LNAI), vol. 5254, pp. 154–168. Springer, Heidelberg (2008)Google Scholar