A strong law of large numbers for non-additive probabilities. (English) Zbl 1266.60051

Chen, Zengjing; Wu, Panyu; Li, Baoming

Int. J. Approx. Reasoning 54, No. 3, 365-377 (2013).

Summary: In this paper, with the notion of independence for random variables under upper expectations, we derive a strong law of large numbers for non-additive probabilities. This result is a natural extension of the classical Kolmogorov’s strong law of large numbers to the case where the probability is no longer additive. As an application of our result, we give most frequent interpretation for Bernoulli-type experiments with ambiguity.

MSC:

60F15	Strong limit theorems
60A86	Fuzzy probability

Keywords:

non-additive probability; strong law of large numbers; independence; upper expectation; Bernoulli experiment