Open Access
February, 1980 On Coding a Stationary Process to Achieve a Given Marginal Distribution
John C. Kieffer
Ann. Probab. 8(1): 131-141 (February, 1980). DOI: 10.1214/aop/1176994829


The problem of coding a stationary process $\{X_i\}^\infty_{i=-\infty}$ onto a stationary process $\{Y_i\}^\infty_{i=-\infty}$ so that for some positive integer $m, (Y_0, Y_1, \cdots, Y_{m-1})$ has a given marginal distribution is considered. The problem is solved for $\{X_i\}$ nonergodic as well as ergodic. The associated universal coding problem is also solved, where one seeks to find a coding function which yields the desired marginal distribution for each member of a class of possible distributions for $\{X_i\}$.


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John C. Kieffer. "On Coding a Stationary Process to Achieve a Given Marginal Distribution." Ann. Probab. 8 (1) 131 - 141, February, 1980.


Published: February, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0426.60036
MathSciNet: MR556419
Digital Object Identifier: 10.1214/aop/1176994829

Primary: 28A65
Secondary: 60G10

Keywords: Ergodic decomposition , ergodic process , mixing invariant marginal , Stationary aperiodic process , stationary coding

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 1 • February, 1980
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