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Keywords:
law of large numbers; uncertain random variable; Etemadi type theorem; Marcinkiewicz–Zygmund type theorem
law of large numbers; uncertain random variable; Etemadi type theorem; Marcinkiewicz–Zygmund type theorem
Summary:
The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically distributed random variables and uncertain variables without satisfying the conditions of regular, independent and identically distributed (IID). Two kinds of Marcinkiewicz-Zygmund type LLNs for uncertain random variables were established in the case of $p \in (0, 1)$ by the second theorem, and in the case of $p > 1$ by the third theorem, respectively. For better illustrating of LLNs for uncertain random variables, some examples were stated and explained. Compared with the existed theorems of LLNs for uncertain random variables, our theorems are the generalised results.
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