SFB 303 Discussion Paper No. B - 51

Author: Schürger, Klaus
Title: On Derriennic's almost Subadditive Ergodic Theorem
Abstract: Recently, Moulin-Ollagnier (1983) derived a new mean ergodic theorem which might be called an almost subadditive ergodic theorem. This allows a fairly simple proof of the L1-part of the Shannon-McMillan-Breiman theorem of information theory (cf. (1983)). Shortly after, Derriennic (1983) showed that Moulin-Ollagnier's mean ergodic theorem holds under weaker moment conditions and that it can be extended to yield an individual ergodic theorem. This, in turn, allows a simple (martingale-free) proof of the almost sure part of the Sannon- Mcmillan-Breiman result. Derriennic's (1983) almost subadditive ergodic theorem is an interesting generalization of Kingman's (1968) ergodic theorem, and might be considered a stochastic analogue of the simple result on real sequences which are „almost subadditive“, shown in this paper.
Creation-Date: December 1986
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