A new strong invariance principle for sums of independent random vectors

被引：1

作者：

Einmahl U. ^{[1
]}

机构：

[1] Department of Mathematics, Free University of Brussel (VUB), Brussel

来源：

Journal of Mathematical Sciences | 2009年 / 163卷 / 4期

关键词：

Random Vector; Invariance Principle; Strong Invariance; Absolute Moment; Independent Random Vector;

D O I：

10.1007/s10958-009-9676-8

中图分类号：

学科分类号：

摘要：

We provide a strong invariance principle for sums of independent, identically distributed random vectors that need not have finite second absolute moments. Various applications are indicated. In particular, we show how one can re-obtain some recent LIL type results from this invariance principle. Bibliography: 16 titles. © 2009 Springer Science+Business Media, Inc.

引用

页码：311 / 327

页数：16

共 16 条

[1]

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[2]

Bhatia R., Matrix Analysis, (1997)

[3]

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[4]

Einmahl U., A useful estimate in the multidimensional invariance principle, Probab. Theory Relat. Fields, 76, pp. 81-101, (1987)

[5]

Einmahl U., Extensions of results of Komlós, Major, and Tusnády to the multivariate case, J. Multivar. Anal., 28, pp. 20-68, (1989)

[6]

Einmahl U., A generalization of Strassen's functional LIL, J. Theor. Probab., 20, pp. 901-915, (2007)

[7]

Einmahl U., Li D., Some results on two-sided LIL behavior, Ann. Probab., 33, pp. 1601-1624, (2005)

[8]

Einmahl U., Li D., Characterization of LIL behavior in Banach space, Trans. Amer. Math. Sac., 360, pp. 6677-6693, (2008)

[9]

Einmahl U., Mason D.M., Rates of clustering in Strassen's LIL for partial sum processes, Probab. Theory Relat. Fields, 97, pp. 479-487, (1993)

[10]

Komlos J., Major P., Tusnady G., An approximation of partial sums of independent, Z. Wahrsch. Verw. Gebiete, 34, pp. 33-58, (1976)

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