关于\(\varphi -\)混合随机变量加权和的完全收敛性与完全矩收敛性
On complete convergence and complete moment convergence for weighted sums of -mixing random variables.
作者信息
Chen Pingyan, Sung Soo Hak
机构信息
1Department of Mathematics, Jinan University, Guangzhou, China.
2Department of Applied Mathematics, Pai Chai University, Daejeon, South Korea.
出版信息
J Inequal Appl. 2018;2018(1):121. doi: 10.1186/s13660-018-1710-2. Epub 2018 Jun 1.
Let , , and with . Let be an array of constants satisfying , and let be a sequence of identically distributed -mixing random variables. For each of the three cases , , and , we provide moment conditions under which We also provide moment conditions under which where . Our results improve and generalize those of Sung (Discrete Dyn. Nat. Soc. 2010:630608, 2010) and Wu et al. (Stat. Probab. Lett. 127:55-66, 2017).
设(a_n)、(b_n)以及(c_n)，且(c_n\neq0)。设({k_n})是一组满足(k_n\rightarrow\infty)的常数数组，设({X_{n}})是一列同分布的(\alpha)-混合随机变量。对于三种情形(a_n = o(b_n))、(a_n\sim b_n)以及(a_n\gg b_n)中的每一种，我们给出了使得(\cdots)成立的矩条件。我们还给出了使得(\cdots)成立的矩条件，其中(\cdots)。我们的结果改进并推广了Sung（《离散动力学自然科学》2010：630608，2010）以及Wu等人（《统计与概率快报》127：55 - 66，2017）的结果。
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