## The Annals of Probability

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

### On Coding a Stationary Process to Achieve a Given Marginal Distribution

#### 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