【摘要】 对一列独立同分布平方可积的随机变量序列{X_n,n≥1},当随机变量的分布具有中尾分布时,讨论了其截断和T_n(a)的随机乘积的渐近正态性质,其中T_n(a)=S_n-S_n(a),n= 1,2,…,S_n(a)=sum from j=1 to n X_jI{M_n-a<X_j≤M_n},a为某一大于零的常数,M_n={X_k}.更多还原

【Abstract】 Let{X_n,n≥1}be a sequence of i.i.d square integrable random variables with continuous distribution function,and let M_n=max{X₁,X₂,…,X_n},for a fixed constant a>0,let S_n（a）=sum from i=1 to n X_jI{M_n-a<X_j≤Mn},and T_n（a）=S_n-S_n（a）.Under the additional condition that the distribution is general medium tailed,the asymptotic distribution of the random product of T_n（a） is given.更多还原