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On the rate of convergence in the global central limit theorem for random sums of uniformly strong mixing random variables
Lithuanian Mathematical Journal ( IF 0.5 ) Pub Date : 2020-05-19 , DOI: 10.1007/s10986-020-09483-9
Jonas Kazys Sunklodas

We present upper bounds of the integral ∫ − ∞ ∞ x l P Z N < x − Φ x d x $$ {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\mathrm{P}\left\{{Z}_N 0 S N X 1 + … + X N $$ \mathrm{E}{S}_N^2>0\left({S}_N{X}_1+\dots +{X}_N\right) $$ of centered random variables X 1 ,X 2 , . . . satisfying the uniformly strong mixing condition. The number of summands N is a nonnegative integer-valued random variable independent of X 1 ,X 2 , . . . .

中文翻译:

关于均匀强混合随机变量的随机和的全局中心极限定理的收敛速度

我们给出积分 ∫ − ∞ ∞ xl PZN < x − Φ xdx $$ {\int}_{-\infty}^{\infty }{\left|x\right|}^l\left|\ mathrm{P}\left\{{Z}_N0 SNX 1 + … + XN $$ \mathrm{E}{S}_N^2>0\left({S}_N{X}_1+\dots +{X}_N\right) $$ 的中心随机变量 X 1 , X 2 , . . . 满足均匀强混合条件。被加数的数目 N 是一个与 X 1 ,X 2 , 无关的非负整数值随机变量。. . .
更新日期:2020-05-19
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