Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • Strong law of large numbers
  • maximum partial sums
  • complete convergence
  • random set
  • embedding method

Mathematics Subject Classification

28B20, 60F15, 54A20

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Suggested citation

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 25 (2018), No. 3, 841–860. https://doi.org/10.68381/jca25057

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Published by Heldermann Verlag, 2018. Rights now held by Banach Press LLC.