Concentration Inequalities and Laws of Large Numbers under Epistemic Irrelevance

Abstract

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent inequalities and laws of large numbers. The proofs indicate connections between concepts of irrelevance for lower/upper expectations and the standard theory of martingales.

arXiv commentThis is a revised version of a paper presented at the International Symposium on Imprecise Probability: Theories and Applications, 2009