# Analytic Variations on Redundancy Rates of Renewal Processes

1 ALGO - Algorithms
Inria Paris-Rocquencourt
Abstract : Csiszár and Shields have recently proved that the minimax redundancy for a class of renewal processes is $\Theta(\sqrt{n})$ where $n$ is the block length. This interesting result provides a first non-trivial bound on redundancy for a non-parametric family of processes. The present paper provides a precise estimate up to the constant term of the redundancy rate for such sources. The asymptotic expansion is derived by complex--analytic methods that include generating function representations, Mellin ransforms, singularity analysis and saddle point estimates. This work places itself within the framework of analytic information theory.
Keywords :
Type de document :
Rapport
[Research Report] RR-3553, INRIA. 1998
Domaine :

https://hal.inria.fr/inria-00073130
Contributeur : Rapport de Recherche Inria <>
Soumis le : mercredi 24 mai 2006 - 11:56:52
Dernière modification le : vendredi 25 mai 2018 - 12:02:02
Document(s) archivé(s) le : jeudi 24 mars 2011 - 12:30:05

### Identifiants

• HAL Id : inria-00073130, version 1

### Citation

Philippe Flajolet, Wojtek Szpankowski. Analytic Variations on Redundancy Rates of Renewal Processes. [Research Report] RR-3553, INRIA. 1998. 〈inria-00073130〉

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