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The moments of the maximum of normalized partial sums related to laws of the iterated logarithm under the sub-linear expectation
Statistics & Probability Letters ( IF 0.9 ) Pub Date : 2022-05-27 , DOI: 10.1016/j.spl.2022.109542
Li-Xin Zhang

Let {Xn;n1} be a sequence of independent and identically distributed random variables on a sub-linear expectation space (Ω,,Ê), Sn=X1++Xn. We consider the moments of maxn1|Sn|/2nloglogn. The sufficient and necessary conditions for the moments to be finite are given. As an application, we obtain the law of the iterated logarithm for moving average processes of independent and identically distributed random variables.



中文翻译:

次线性期望下与迭代对数定律相关的归一化部分和最大值的矩

{Xn;n1}是亚线性期望空间上的独立同分布随机变量序列(Ω,,̂),小号n=X1++Xn. 我们考虑的时刻最大限度n1|小号n|/2n日志日志n. 给出了矩为有限的充分必要条件。作为应用,我们得到了独立同分布随机变量的移动平均过程的迭代对数定律。

更新日期:2022-06-01
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