Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences
Asymptotics for Self-Normalized Random Products of Sums for Mixing Sequences
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DOI：
10.1080/07362990601139487
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发表时间：
2007-02
影响因子：
1.3
通讯作者：
Weidong Liu;Zhengyan Lin
中科院分区：
文献类型：
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作者：
Weidong Liu;Zhengyan Lin
设{X，Xn，n≥1}为严格平稳的φ混合正态随机变量序列，tn为正整数随机变量，记为，且E X=μ>；0.在关于tn和的一般条件下，我们证明了部分和的自归一化随机积仍然是渐近对数正态的。
Abstract Let {X, X n , n ≥ 1} be a sequence of a strictly stationary φ-mixing positive random variables, which is in the domain of attraction of the normal law, and t n be a positive, integer random variable and denote , , and E X = μ > 0. Under a general condition about t n and , we show that the self-normalized random products of the partial sums, , is still asymptotically lognormal.