Geodesic
Complete Convergence and Strong Laws of Large Numbers for Double Arrays of Convex Compact Integrable Random Sets and Applications for Random Fuzzy Variables
Journal of convex analysis, Tome 25 (2018) no. 3, pp. 841-86
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We prove some fairly general results of the complete convergence for maximum partial double sums and strong law of large numbers for double arrays of real and Banach valued random variables. Then using the norm compactness of the expectation of convex compact integrable random sets and an embedding method, we improve several results for maximum partial double sums of convex compact integrable random sets under some new conditions on the support functions. We also provide a typical example illustrating this study. Further applications to the strong law of large numbers for random fuzzy convex upper semicontinuous variables are given.
Classification : 28B20, 60F15, 54A20
Mots-clés : Strong law of large numbers, maximum partial sums, complete convergence, random set, embedding method 
@article{JCA_2018_25_3_JCA_2018_25_3_a7,
     author = {N. V. Quang and H. T. Duyen},
     title = {Complete {Convergence} and {Strong} {Laws} of {Large} {Numbers} for {Double} {Arrays} of {Convex} {Compact} {Integrable} {Random} {Sets} and {Applications} for {Random} {Fuzzy} {Variables}},
     journal = {Journal of convex analysis},
     pages = {841--86},
     year = {2018},
     volume = {25},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a7/}
}
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N. V. Quang; H. T. Duyen. Complete Convergence and Strong Laws of Large Numbers for Double Arrays of Convex Compact Integrable Random Sets and Applications for Random Fuzzy Variables. Journal of convex analysis, Tome 25 (2018) no. 3, pp. 841-86. http://geodesic.mathdoc.fr/item/JCA_2018_25_3_JCA_2018_25_3_a7/