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

作     者：Debowski, Lukasz 

作者机构：Ctr Wiskunde & Informat NL-1098 XG Amsterdam Netherlands 

出 版 物：《JOURNAL OF THEORETICAL PROBABILITY》 (J. Theor. Probab.)

年 卷 期：2010年第23卷第1期

页      面：237-256页

核心收录：

学科分类：07[理学] 0714[理学-统计学（可授理学、经济学学位）] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Polish Ministry of Scientific Research and Information Technology [1/P03A/045/28] PASCAL II Network of Excellence [IST-2002-506778] 

主　　题：Asymptotically mean stationary processes Variable-length coding Synchronization Shift-invariant algebras Complete fix-free sets Finite-energy processes Block entropy 

摘      要：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 sigma-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.