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Induced transformations of recurrent a.m.s. dynamical systems
KTH, School of Electrical Engineering (EES), Communication Theory.
KTH, School of Electrical Engineering (EES), Communication Theory.ORCID iD: 0000-0002-7926-5081
2015 (English)In: Stochastics and Dynamics, ISSN 0219-4937, Vol. 15, no 02Article in journal (Refereed) Published
Abstract [en]

This note proves that an induced transformation with respect to a finite measure set of a recurrent asymptotically mean stationary dynamical system with a sigma-finite measure is asymptotically mean stationary. Consequently, the Shannon–McMillan–Breiman theorem, as well as the Shannon–McMillan theorem, holds for all reduced processes of any finite-state recurrent asymptotically mean stationary random process.

As a by-product, a ratio ergodic theorem for asymptotically mean stationary dynamical systems is presented.

Place, publisher, year, edition, pages
2015. Vol. 15, no 02
National Category
Probability Theory and Statistics
Research subject
URN: urn:nbn:se:kth:diva-160642DOI: 10.1142/S0219493715500100ISI: 000352316600004OAI: diva2:790793
Swedish Research Council

QC 20150519

Available from: 2015-02-25 Created: 2015-02-25 Last updated: 2015-05-19Bibliographically approved

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Huang, ShengSkoglund, Mikael
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