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 -