# 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.
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https://hal.inria.fr/inria-00073130
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Submitted on : Wednesday, May 24, 2006 - 11:56:52 AM
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### Identifiers

• 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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