Induced transformations of recurrent a.m.s. dynamical systems
2015 (English)In: Stochastics and Dynamics, ISSN 0219-4937, Vol. 15, no 02Article in journal (Refereed) Published
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
Probability Theory and Statistics
Research subject Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-160642DOI: 10.1142/S0219493715500100ISI: 000352316600004OAI: oai:DiVA.org:kth-160642DiVA: diva2:790793
FunderSwedish Research Council
QC 201505192015-02-252015-02-252015-05-19Bibliographically approved