Analytic variations on redundancy rates of renewal processes

Csiszar and Shields (1996) proved that the minimax redundancy for a class of (stationary) renewal processes is /spl Theta/(/spl radic/n) where n is the block length. This interesting result provides a nontrivial bound on redundancy for a nonparametric family of processes. The present paper gives a precise estimate of the redundancy rate for such (nonstationary) renewal sources, namely, 2/(log2)/spl radic/((/spl pi//sup 2//6-1)n)+O(log n). This asymptotic expansion is derived by complex-analytic methods that include generating function representations, Mellin transforms, singularity analysis. and saddle-point estimates. This work places itself within the framework of analytic information theory.