# Entropy of probability kernels from the backward tail boundary

Studia Mathematica (2015)

- Volume: 227, Issue: 3, page 249-257
- ISSN: 0039-3223

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topTim Austin. "Entropy of probability kernels from the backward tail boundary." Studia Mathematica 227.3 (2015): 249-257. <http://eudml.org/doc/285446>.

@article{TimAustin2015,

abstract = {
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.
},

author = {Tim Austin},

journal = {Studia Mathematica},

keywords = {probability kernel; tail boundary; operator entropy},

language = {eng},

number = {3},

pages = {249-257},

title = {Entropy of probability kernels from the backward tail boundary},

url = {http://eudml.org/doc/285446},

volume = {227},

year = {2015},

}

TY - JOUR

AU - Tim Austin

TI - Entropy of probability kernels from the backward tail boundary

JO - Studia Mathematica

PY - 2015

VL - 227

IS - 3

SP - 249

EP - 257

AB -
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.

LA - eng

KW - probability kernel; tail boundary; operator entropy

UR - http://eudml.org/doc/285446

ER -

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