Entropy of probability kernels from the backward tail boundary

• Autorzy: Tim Austin
• Języki publikacji: EN

Abstrakty

EN

A number of recent works have sought to generalize the Kolmogorov-Sinai entropy of probability-preserving transformations to the setting of Markov operators acting on the integrable functions on a probability space (X,μ). These works have culminated in a proof by Downarowicz and Frej that various competing definitions all coincide, and that the resulting quantity is uniquely characterized by certain abstract properties.
On the other hand, Makarov has shown that this 'operator entropy' is always dominated by the Kolmogorov-Sinai entropy of a certain classical system that may be constructed from a Markov operator, and that these numbers coincide under certain extra assumptions. This note proves that equality in all cases.

Kategorie tematyczne

• 37A50: Relations with probability theory and stochastic processes
• 37A30: Ergodic theorems, spectral theory, Markov operators
• 60J05: Discrete-time Markov processes on general state spaces
• 37A35: Entropy and other invariants, isomorphism, classification

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 227
• Numer: 3
• Strony: 249-257

Daty

wydano

2015

Twórcy

autor

Tim Austin

• Courant Institute of Mathematical Sciences, New York University, 251 Mercer St, New York, NY 10012, U.S.A.

Identyfikatory

DOI

10.4064/sm227-3-4