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

PB - Springer

CY - Berlin

T2 - 19th International Conference, ALT 2008

Y2 - 31 December 2008

ER -