In this paper we define the expected value of a random vector with respect to a set-valued probability measure. The concepts of independent and identically distributed random vectors are appropriately defined, and a strong law of large numbers is derived in this setting. Finally, an example of a set-valued probability useful in Bayesian inference is provided.
Publié le : 1983-11-14
Classification:
Set-valued measure,
strong law of large numbers,
interval of measures,
60B12,
60F15
@article{1176993455,
author = {Puri, Madan L. and Ralescu, Dan A.},
title = {Strong Law of Large Numbers with Respect to a Set-Valued Probability Measure},
journal = {Ann. Probab.},
volume = {11},
number = {4},
year = {1983},
pages = { 1051-1054},
language = {en},
url = {http://dml.mathdoc.fr/item/1176993455}
}
Puri, Madan L.; Ralescu, Dan A. Strong Law of Large Numbers with Respect to a Set-Valued Probability Measure. Ann. Probab., Tome 11 (1983) no. 4, pp. 1051-1054. http://gdmltest.u-ga.fr/item/1176993455/