### Abstract

The asymptotic a.s.-relation [eqution presented] is derived for any finite-valued stationary ergodic process X=(X_{n}, n ∈Z) that satisfies a Doeblin-type condition: there exists r ≥ 1 such that [eqution presented]. Here, H is the entropy rate of the process X, and L_{i}
^{n}(X) is the length of a shortest prefix in X which is initiated at time i and is not repeated among the prefixes initiated at times j, 1 ≤ i ≠ J ≤ n. The validity of this limiting result was established by Shields in 1989 for i.i.d. processes and also for irreducible aperiodic Markov chains. Under our new condition, we prove that this holds for a wider class of processes, that may have infinite memory.

Original language | English (US) |
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Title of host publication | Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994 |

Number of pages | 1 |

DOIs | |

State | Published - Dec 1 1994 |

Event | 1994 IEEE International Symposium on Information Theory, ISIT 1994 - Trondheim, Norway Duration: Jun 27 1994 → Jul 1 1994 |

### Other

Other | 1994 IEEE International Symposium on Information Theory, ISIT 1994 |
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Country | Norway |

City | Trondheim |

Period | 6/27/94 → 7/1/94 |

### All Science Journal Classification (ASJC) codes

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

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## Cite this

*Proceedings - 1994 IEEE International Symposium on Information Theory, ISIT 1994*[394774] https://doi.org/10.1109/ISIT.1994.394774