On Instability of the Ergodic Limit Theorems with Respect to Small Violations of Algorithmic Randomness

2011/05/21 by V'yugin, Vladimir
#68Q30 03D32 #FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1105.4274

Abstract

An instability property of the Birkhoff's ergodic theorem and related asymptotic laws with respect to small violations of algorithmic randomness is studied. The Shannon--McMillan--Breiman theorem and all universal compression schemes are also among them.

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