Strong Stability of Linear Forms in φ-Mixing Random Variables

摘要

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 {a n , n≥ 1}and {b n , n≥1 }there exist d n∈ R, n=1,2,…, such that b-1n sum from i=1 to n() aixi-dn→0 a.s.under some suitable conditions. The results extend and improvethe corresponding theorems for independent identically distributedrandom variables.