### Abstract

We obtain bounds on the probability that the n′th variable in a stationary random process differs from all previous ones, and use it to show that the pattern entropy rate of any finite-entropy stationary process equals the process entropy rate. In the particular case of i.i.d. processes we also bound the speed at which the per-symbol pattern entropy converges to the sequence entropy.

Original language | English (US) |
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Title of host publication | Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05 |

Pages | 2203-2207 |

Number of pages | 5 |

DOIs | |

State | Published - Dec 1 2005 |

Event | 2005 IEEE International Symposium on Information Theory, ISIT 05 - Adelaide, Australia Duration: Sep 4 2005 → Sep 9 2005 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2005 |

ISSN (Print) | 2157-8099 |

### Other

Other | 2005 IEEE International Symposium on Information Theory, ISIT 05 |
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Country | Australia |

City | Adelaide |

Period | 9/4/05 → 9/9/05 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

Orlilsky, A., Santhanam, N. P., Viswanalhan, K., & Zhang, J. (2005). Innovation and pattern entropy of stationary processes. In

*Proceedings of the 2005 IEEE International Symposium on Information Theory, ISIT 05*(pp. 2203-2207). [1523738] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2005). https://doi.org/10.1109/ISIT.2005.1523738