Journal of Convex Analysis 25 (2018), No. 3, 841--860
Copyright Heldermann Verlag 2018
Complete Convergence and Strong Laws of Large Numbers for Double Arrays of Convex Compact Integrable Random Sets and Applications for Random Fuzzy Variables
Nguyen Van Quang
Institute for Computational Science and Technology (ICST), Ho Chi Minh City, Vietnam
and: Vinh University, Nghe An Province, Vietnam
nvquang@hotmail.com
Hoang Thi Duyen
Quang Binh University, Quang Binh Province, Vietnam
hoangduyen267@gmail.com
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.
Keywords: Strong law of large numbers, maximum partial sums, complete convergence, random set, embedding method.
MSC: 28B20, 60F15, 54A20
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