Shannon entropy for stationary processes and dynamical systems

Details Shannon entropy for stationary processes and dynamical systems Shannon entropy for stationary processes and dynamical systems

2007-01-08

arxiv.org/abs/math/0701229v1

Mathematics

Dynamical Systems

53 pages

Scientific paper

We consider stationary ergodic processes indexed by $\mathbb Z$ or $\mathbb
Z^n$ whose finite dimensional marginals have laws which are absolutely
continuous with respect to Lebesgue measure. We define an entropy theory for
these continuous processes, prove an analog of the Shannon Breiman Mac Millan
theorem and study more precisely the particular example of Gaussian processes.

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