Abstract
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 {xn, n ⩾ 1} and two sequences of positive numbers {an, n ⩾ 1} and {bn, n ⩾ 1} there exist dn ∈ R, n = 1,2,L, such that \( b_n^{ - 1} \sum\limits_{i = 1}^n {a_i x_i - d_n \to 0} \) a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.
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