Asymptotics for self-normalized random products of sums of i.i.d. random variables

作者：Pang, Tian-Xiao^*; Lin, Zheng-Yan; Hwang, Kyo-Shin

来源：Journal of Mathematical Analysis and Applications, 2007, 334(2): 1246-1259.

DOI：10.1016/j.jmaa.2006.12.085

• self-normalized
• products
• domain of attraction of the normal law
• lognormal distribution
• i.i.d. random variables

Let {X, X-i; i >= 1} be a sequence of independent and identically distributed positive random variables, which is in the domain of attraction of the normal law, and t(n) be a positive, integer random variable. Denote S-n = Sigma(n)(i=1) X-i, V-n(2) = Sigma(n)(i=1) (X-i - (X) over bar)(2), where (X) over bar denotes the sample mean. Then we show that the self- normalized random product of the partial sums, (Pi(ln)(k=1) S-k/k mu)(mu/Vtn), is still asymptotically lognormal under a suitable condition about t(n).

• 出版日期2007-10-15
• 单位浙江大学