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 {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 \( b_n^{ - 1} \sum\limits_{i = 1}^n {a_i x_i - d_n \to 0} \) a.s. under some suitable conditions. The results extend and improve the corresponding theorems for independent identically distributed random variables.
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Foundation item: Supported by the National Natural Science Foundation of China(10671149)
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Gan, S. Strong stability of linear forms in φ-mixing random variables. Wuhan Univ. J. Nat. Sci. 14, 6–10 (2009). https://doi.org/10.1007/s11859-009-0102-3
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DOI: https://doi.org/10.1007/s11859-009-0102-3