A New Law of the Iterated Logarithm in Rd with Application to Matrix-Normalized Sums of Random Vectors

Valery Koval ()
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Valery Koval: Zhytomyr Institute of Engineering and Technology

Journal of Theoretical Probability, 2002, vol. 15, issue 1, 249-257

Abstract: 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 , n≥1. Application to matrix-normalized sums of independent random vectors is given.

Keywords: law of the iterated logarithm; sums of independent random vectors; matrix normings; rates of convergence in the CLT (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1013851720494

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