Facebook Instagram Twitter RSS Feed PodBean Back to top on side

Precise rates in the law of iterated logarithm for the moment convergence of $φ$-mixing sequences

In: Mathematica Slovaca, vol. 65, no. 6
Xiao-Yong Xiao - Hong-Wei Yin
Detaily:
Rok, strany: 2015, 1571 - 1588
Kľúčové slová:
precise asymptotics, moment convergence, the law of iterated logarithm, $\varphi$\nbd-mixing
O článku:
Let $\{Xn| n≥1\}$ be a strictly stationary sequence of $φ$-mixing random variables with zero mean and finite variance. Set $Sn=∑i=1n Xi$ and $Mn=\max1≤ k≤ n|Sk|$, $n≥1$. For $d>0$ and $an=o(( log log n)-d)$, we show the exact rates in the law of iterated logarithm of a kind of weighted infinite series of $E\{|Sn|-(ε+an)σ\sqrt{n}( log log n)d\}+$ and $E\{Mn-(ε+an)σ\sqrt{n}( log log n)d\}+$ as $ε\searrow 0$.
Ako citovať:
ISO 690:
Xiao, X., Yin, H. 2015. Precise rates in the law of iterated logarithm for the moment convergence of $φ$-mixing sequences. In Mathematica Slovaca, vol. 65, no.6, pp. 1571-1588. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0107

APA:
Xiao, X., Yin, H. (2015). Precise rates in the law of iterated logarithm for the moment convergence of $φ$-mixing sequences. Mathematica Slovaca, 65(6), 1571-1588. 0139-9918. DOI: https://doi.org/10.1515/ms-2015-0107
O vydaní:
Publikované: 1. 12. 2015