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Precise rates in the law of logarithm for i.i.d. random variables

โœ Scribed by Tian-Xiao Pang; Zheng-Yan Lin

Publisher
Elsevier Science
Year
2005
Tongue
English
Weight
559 KB
Volume
49
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

Let {x,x~

; n >\_ 1} be a sequence of i.i.d, random variables. Set Sn = X1 + X2 + โ€ข .. +Xn and M,~ = maxk 1. By using the strong approximation method, we obtain that for any -1
if and only if EX = 0 and EX 2 < oo, which strengthen and extend the result of Gut and Sp~taru [1],
where N is the standard normal random variable. Furthermore, L2 convergence and a.s. convergence are also discussed.

๐Ÿ“œ SIMILAR VOLUMES

The moderate deviation principle for sel
The moderate deviation principle for self-normalized sums of sums of i.i.d. random variables
โœ Bin Qian; Jun Yan ๐Ÿ“‚ Article ๐Ÿ“… 2009 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 326 KB

The corresponding moderate deviation principle follows. The Central Limit theorem has been recently obtained by Pang, Lin and Hwang [T.X. Pang, Z.Y. Lin, K.S. Hwang, Asymptotics for self-normalized random products of sums of i.i.d. random variables, J. Math. Anal. Appl. 334 (2007) 1246-1259].

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Let \(\left\{X, X_{n} ; \vec{n} \in \mathbb{N}^{d}\right\}\) be a field of independent identically distributed real random variables, \(0<p<2\), and \(\left\{a_{\bar{n}, \bar{k}} ;(\bar{n}, \bar{k}) \in \mathbb{N}^{d} \times \mathbb{N}^{d}, \bar{k} \leqslant \bar{n}\right\}\) a triangular array of r