On strong law of large numbers for weakly stationary $\varphi$-mixing set-valued random variable sequences

Luc Tri Tuyen

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arXiv · 2601.09197

On strong law of large numbers for weakly stationary $\varphi$-mixing set-valued random variable sequences

Luc Tri Tuyen

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Abstract

In this paper we extend the notion of $\varphi$-mixing to set-valued random sequences that take values in the family of closed subsets of a Banach space. Several strong laws of large numbers for such $\varphi$-mixing sequences are stated and proved. Illustrative examples show that the hypotheses of the theorems are both natural and sharp.

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Luc Tri Tuyen. 2026-01-14. On strong law of large numbers for weakly stationary $\varphi$-mixing set-valued random variable sequences. https://arxiv.org/abs/2601.09197

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