A New Law of the Iterated Logarithm in Rd with Application to Matrix-Normalized Sums of Random Vectors |
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| Authors: | Valery Koval |
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| Institution: | (1) Department of Mathematics, Zhytomyr Institute of Engineering and Technology, Cherniakhovsky 103, Zhytomyr, 10005, Ukraine |
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| Abstract: | Let (X
n
, n 1) be a sequence of independent centered random vectors in R
d
. We study the law of the iterated logarithm lim sup
n  (2 log log  B
n
)–1/2 B
–1/2
n
S
n
=1 a.s., where B
n
is the covariance matrix of S
n
=
n
i=1
X
i
, n1. Application to matrix-normalized sums of independent random vectors is given. |
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| Keywords: | law of the iterated logarithm sums of independent random vectors matrix normings rates of convergence in the CLT |
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