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 be a sequence of independent centered random vectors in with finite moments of order and let be a sequence of matrices. We find explicit conditions under which

**1.**Valery Koval,*A new law of the iterated logarithm in 𝑅^{𝑑} with application to matrix-normalized sums of random vectors*, J. Theoret. Probab.**15**(2002), no. 1, 249–257. MR**1883931**, 10.1023/A:1013851720494**2.**V. V. Buldygin and V. A. Koval,*Convergence to zero and boundedness of operator-normed sums of random vectors with application to autoregression processes*, Georgian Math. J.**8**(2001), no. 2, 221–230. Dedicated to Professor Nicholas Vakhania on the occasion of his 70th birthday. MR**1851031**

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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

Email:
vkoval@com.zt.ua

DOI:
https://doi.org/10.1090/S0094-9000-06-00665-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