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In this paper some new results of strong stability of linear forms in φ-mixing random variables are given. It is mainly proved that for a sequence of φ-mixing random variables {x n , n ⩾ 1} and two sequences of positive numbers {a n , n ⩾ 1} and {b n , n ⩾ 1} there exist d n ∈ R, n = 1,2,L, such that bₙ- 1 ∑i = 1ⁿ aᵢ xᵢ - dₙ → 0 a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.
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Gan Shixin (2009) studied this question.
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