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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)


Bounded law of the iterated logarithm for sums of independent random vectors normalized by matrices

Author: V. O. Koval'
Translated by: Oleg Klesov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 72 (2005).
Journal: Theor. Probability and Math. Statist. 72 (2006), 69-73
MSC (2000): Primary 60F15
Published electronically: August 18, 2006
MathSciNet review: 2168137
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ (X_n,n\geq 1)$ be a sequence of independent centered random vectors in  $ \mathbf R^d$ with finite moments of order $ p\in(2,3]$ and let $ (A_n,n\geq 1)$ be a sequence of $ m\times d$ matrices. We find explicit conditions under which

$\displaystyle \limsup_{n\to\infty} c_n \left\Vert A_n\sum_{i=1}^n X_i\right\Vert<\infty $

almost surely, where $ (c_n,n\geq 1)$ is some sequence of positive numbers.

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Additional Information

V. O. Koval'
Affiliation: Department of Higher Mathematics, Zhitomir State University for Technology, Chernyakhovskiĭ Street 103, 10005 Zhitomir, Ukraine

PII: S 0094-9000(06)00665-X
Keywords: Law of the iterated logarithm, sums of independent random vectors, matrix normalizations
Received by editor(s): August 31, 2004
Published electronically: August 18, 2006
Article copyright: © Copyright 2006 American Mathematical Society

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