The Annals of Probability

On Coding a Stationary Process to Achieve a Given Marginal Distribution

John C. Kieffer

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Abstract

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 $\{X_i\}$.

Article information

Source
Ann. Probab., Volume 8, Number 1 (1980), 131-141.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176994829

Digital Object Identifier
doi:10.1214/aop/1176994829

Mathematical Reviews number (MathSciNet)
MR556419

Zentralblatt MATH identifier
0426.60036

JSTOR
links.jstor.org

Subjects
Primary: 28A65
Secondary: 60G10: Stationary processes

Keywords
Stationary aperiodic process ergodic process stationary coding mixing invariant marginal ergodic decomposition

Citation

Kieffer, John C. On Coding a Stationary Process to Achieve a Given Marginal Distribution. Ann. Probab. 8 (1980), no. 1, 131--141. doi:10.1214/aop/1176994829. https://projecteuclid.org/euclid.aop/1176994829


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