Journal of Convex Analysis 24 (2017), No. 1, 213--238
Copyright Heldermann Verlag 2017
Convergence of Weighted Sums and Strong Law of Large Numbers for Convex Compact Integrable Random Sets and Fuzzy Random Sets
Nguyen Van Quang
Vinh University, Nghe An Province, Vietnam
nvquang@hotmail.com
Hoang Thi Duyen
Quang Binh University, Quang Binh Province, Vietnam
hoangduyen267@gmail.com
We prove several results in the a.s. convergence of weighted sums and strong law of large numbers for convex compact integrable random sets in separable Banach spaces via the norm compactness of the expectation of convex compact integrable random sets and an embedding method. The techniques are applied to prove strong law of large numbers for fuzzy random variables and other related results. Tightness conditions are discussed in comparison with earlier results in the literature.
Keywords: Expectation, fuzzy convex, strong law of large numbers, tight, Toeplitz sequence, weighted sum.
MSC: 28B20, 60G42, 46A17, 54A20
[ Fulltext-pdf (201 KB)] for subscribers only.