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arXiv · 0911.5318

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

Łukasz Dębowski
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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.

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Łukasz Dębowski. 2011-02-07. Variable-Length Coding of Two-Sided Asymptotically Mean Stationary Measures. https://doi.org/10.1007/s10959-009-0264-0

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