Statistics for dynamical sources

Abstract

A quite general model of source that comes from dynamical systems theory is introduced. Within this model, basic problems of algorithmic information theory contexts are analysed. The main tool is a new object, a (generalized) transfer operator, which can be viewed as a "generating" operator for "fundamental" probabilities. Its dominant spectral objects are related to important parameters of the source, such as the entropy, and play a central role in all the results.