Law of large numbers for non-additive measures
Yann Rebille
TL;DR
This paper establishes limit theorems, including weak and strong laws of large numbers, for non-additive measures such as balanced and exact games, extending to upper envelope measures.
Contribution
It introduces new limit theorems for classes of non-additive measures, expanding the theoretical understanding of these measures in probabilistic contexts.
Findings
Weak and strong laws of large numbers for balanced games
Sharper results for exact games
Extension of limit theorems to upper envelope measures
Abstract
Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an extension to upper enveloppe measures.
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Taxonomy
TopicsProbability and Statistical Research · Stochastic processes and financial applications