Laws of Large Numbers for Non-Independent Random Variables on Hyperspaces with respect to the Hausdorff Metric

Jinping Zhang; Li Guan

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arXiv · 2011.07199

Laws of Large Numbers for Non-Independent Random Variables on Hyperspaces with respect to the Hausdorff Metric

Jinping Zhang·Li Guan

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Abstract

This paper investigates the limit behavior of the Minkowski sums for sequences of set-valued random variables. When the underlying space is finite dimensional, by using the support function, we establish the weak and strong laws of large numbers for non-independent random variables in the hyperspace with respect to the Hausdorff metric $d_H$.

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Jinping Zhang, Li Guan. 2020-11-14. Laws of Large Numbers for Non-Independent Random Variables on Hyperspaces with respect to the Hausdorff Metric. https://arxiv.org/abs/2011.07199

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