P. Terán, I. Molchanov (2006). In Soft methods for integrated uncertainty modelling (J.Lawry, E.Miranda, A.Bugarin, S.Li, M.A.Gil, P. Grzegorzewski, O. Hryniewicz, editors), 153-160. Springer, Berlin.
[Proceedings of the 3rd Intl. Conf. on Soft Methods in Statistics and Probability] [Invited session Probability of imprecisely valued random elements with applications]
We tried to draw some attention to our JTP paper among the fuzzy community, by showing that spaces of fuzzy sets are examples of the general`convex combination spaces' used there. A c.c.s. is much more general than a Banach space (e.g. convolution of probability measures, max-product, global NPC spaces).
Two applications are presented:
-a strong law of large numbers for fuzzy random variables in non-Banach spaces,
-a strong law of large numbers for level-2 fuzzy random variables.
These results cannot be obtained with the usual methods relying on Banach spaces.
Up the line:
A law of large numbers in a metric space with a convex combination operation (w. Ilya Molchanov). You may download a (non-final) preprint copy from Ilya's website.
Down the line:
Nothing yet. Some of the compactness methods in the proof are reused in
On a uniform law of large numbers for random sets and subdifferentials of random functions.
To download, click on the title or here.
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