Limit law of the iterated logarithm for B-valued trimmed sums
详细信息 查看全文
- 作者：KE-ANG FU ; YUYANG QIU ; YELING TONG
- 关键词：Banach space ; trimmed sums ; the limit law of the iterated logarithm ; 60F15 ; 60G50
- 刊名：Proceedings Mathematical Sciences
- 出版年：2015
- 出版时间：May 2015
- 年：2015
- 卷：125
- 期：2
- 页码：221-225
- 全文大小：99 KB
- 参考文献：[1]Chen X, The limit law of the iterated logarithm, J. Theor. Probab., 2013, (to appear)<br>[2]Fu K A and Zhang L X, A general LIL for trimmed sums of random fields in Banach spaces, Acta Math. Hungar. 122 (2009) 91-03MATH MathSciNet View Article <br>[3]Fu K A, A nonclassical LIL for sums of B-valued random variables when extremes terms are excluded, Acta Math. Hungar. 137 (2012) 1-MATH MathSciNet View Article <br>[4]Kuelbs J and Ledoux M, Extreme values and the laws of the iterated logarithm, Probab. Theory Related Fields 74 (1987) 319-40<br>[5]Kuelbs J and Ledoux M, Extreme values and LIL behavior, Probability in Banach Space VI. Progress in Probability (1990) (Boston: Birkh?user)MATH MathSciNet View Article <br>[6]Ledoux M and Talagrand M, Some applications of isoperimetric methods to strong limit theorems for sums of independent random variables, Ann. Probab. 18 (1990) 754-80MATH MathSciNet View Article <br>[7]Li D L and Liang H Y, The limit law of the iterated logarithm in Banach space, Statist. Probab. Lett. 83 (2013) 1800-804MATH MathSciNet View Article <br>[8]Mori T, The strong law of large numbers when extreme terms are excluded from sums, Z. Wahrsch. Verew. Gebiette 36 (1976) 189-94MATH View Article <br>[9]Mori T, Stability for sums of i.i.d. random variables when extreme terms are excluded, Z. Wahrsch. Verew. Gebiette 40 (1977) 159-67MATH View Article <br>[10]Zhang L X, Strong approximation theorems for sums of random variables when extreme terms are excluded, Acta Math. Sinica, English Series 18 (2002) 311-26<br>[11]Zhang L X, LIL and the approximation of rectangular sums of B-valued random variables when extreme terms are excluded, Acta Math. Sinica, English Series 18 (2002) 605-14MATH View Article <br>
- 作者单位：KE-ANG FU (1) <br> YUYANG QIU (1) <br> YELING TONG (2) <br><br>1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, 310018, China <br> 2. Zhejiang Institute of Traditional Chinese Medicine, Hangzhou, 310028, China <br>
- 刊物类别：Mathematics and Statistics
- 刊物主题：Mathematics<br>Mathematics<br>
- 出版者：Springer India
- ISSN：0973-7685
文摘
Given a sequence of i.i.d. random variables {X,X n ;n?} taking values in a separable Banach space (B, ∥?? with topological dual B ?/sup>, let \(X_{n}^{(r)}=X_{m}\) if ?em class="EmphasisTypeItalic">X m ?is the r-th maximum of {?em class="EmphasisTypeItalic">X k ?1?em class="EmphasisTypeItalic">k?em class="EmphasisTypeItalic">n} and \({}^{(r)}S_{n}=S_{n}-(X_{n}^{(1)}+\cdots +X_{n}^{(r)})\) be the trimmed sums when extreme terms are excluded, where \(S_{n}={\sum }_{k=1}^{n}X_{k}\). In this paper, it is stated that under some suitable conditions, $$\lim _{n\to \infty }\frac {1}{\sqrt {2\log \log n}}\max _{1\le k\le n}\frac {\|^{(r)}S_{k}\|}{\sqrt {k}}=\sigma (X)~~~\mathrm {a.s.},$$