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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
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-160642DOI: 10.1142/S0219493715500100ISI: 000352316600004OAI: oai:DiVA.org:kth-160642DiVA: diva2:790793
Funder
Swedish Research Council
Note

QC 20150519

Available from: 2015-02-25 Created: 2015-02-25 Last updated: 2017-12-04Bibliographically approved

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Skoglund, Mikael

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