Variable-Length Coding of Two-sided Asymptotically Mean Stationary Measures

Łukasz Dębowski ()
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Łukasz Dębowski: Centrum Wiskunde & Informatica

Journal of Theoretical Probability, 2010, vol. 23, issue 1, 237-256

Abstract: Abstract We collect several observations that concern variable-length coding of two-sided infinite sequences in a probabilistic setting. Attention is paid to images and preimages of asymptotically mean stationary measures defined on subsets of these sequences. We point out sufficient conditions under which the variable-length coding and its inverse preserve asymptotic mean stationarity. Moreover, conditions for preservation of shift-invariant σ-fields and the finite-energy property are discussed, and the block entropies for stationary means of coded processes are related in some cases. Subsequently, we apply certain of these results to construct a stationary nonergodic process with a desired linguistic interpretation.

Keywords: Asymptotically mean stationary processes; Variable-length coding; Synchronization; Shift-invariant algebras; Complete fix-free sets; Finite-energy processes; Block entropy; 60G10; 28D99; 94A45; 94A17 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0264-0

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