Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, t...Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P（｜S_n｜ ≥（ε ＋ a_n）σn^（1/2）（log log n）~d）.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.61662037)the Scientific Program of Department of Education of Jiangxi Province(Grant Nos.GJJ150894GJJ150905)
文摘Let {X, X_n, n ≥ 1} be a sequence of i.i.d. random vectors with EX =（0,..., 0）_（m×1） and Cov（X, X） = σ~2 Ⅰ_m, and set S_n =∑_（i=1）~n X_i, n ≥ 1. For every d 〉 0 and a_n =o（（log log n）^（-d））, the article deals with the precise rates in the genenralized law of the iterated logarithm for a kind of weighted infinite series of P（｜S_n｜ ≥（ε ＋ a_n）σn^（1/2）（log log n）~d）.
