A strong law of large numbers for capacities

By Fabio Maccheroni, Massimo Marinacci. 2005

146 citations recorded by the source corpus.

We consider a totally monotone capacity on a Polish space and a sequence of bounded p.i.i.d. random variables. We show that, on a full set, any cluster point of empirical averages lies between the lower and the upper Choquet integrals of the random variables, provided either the random variables or the capacity are continuous.

Subfields: Management Science and Operations Research, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/02c421a72a113f85778d92fa8eab5628d2f92903

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In Management Science and Operations Research

In Mathematical Physics

Citations in the corpus

Limit theorems with rate of convergence under sublinear expectations (2017, background): “See, for example, Walley (1991), Marinacci (1999) and Maccheroni and Marinacci (2005). We adopt the notion introduced by Peng (2010) and say that a random vector Y ∈ R is independent of another random vector X ∈ R if”
SYMMETRY OF EVIDENCE WITHOUT EVIDENCE OF SYMMETRY (2010, background): “Maccheroni and Marinacci [26] assume such pairwise independence (albeit only for acts that are indicator functions).”
Weak and strong laws of large numbers for coherent lower previsions (2008, methodology): “In a similar vein, this analysis allows us to prove in a simple way a significantly more general version of a law of large numbers for completely (or totally) monotone capacities that was first proven by Maccheroni and Marinacci (2005). 9 Indeed, consider a sequence of random variables Xk taking val”
A New Central Limit Theorem under Sublinear Expectations (2008, methodology): “To our knowledge, the law of large numbers with non-additive probability measures have been investigated with a quite different framework and approach from ours (see [9], [10]).”
Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, unknown): “To our knowledge, the law of large numbers with non-additive probability measures have been investigated under a framework and approach quite different from ours, where no convergence in law is obtained (see Marinacci (1999) and Maccheroni & Marinacci (2005)).”
Recursive smooth ambiguity preferences (2009, background): “In Maccheroni, Marinacci, and Rustichini (2006b), they extend variational preferences to an intertemporal setting and also characterize when this extension is dynamically consistent, thus generalizing the characterization of Epstein and Schneider (2003b) for MEU.”
Nonlinear Expectations and Stochastic Calculus under Uncertainty (2010, methodology): “For other types of the related notions of distributions and independence under nonlinear expectations or non-additive probabilities, we refer to the Notes of the book [120] and the references listed in Marinacci (1999) [83] and Maccheroni and Marinacci (2005) [84].”