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

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

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  1. Department of Mathematics, Zhytomyr Institute of Engineering and Technology, Cherniakhovsky 103, Zhytomyr, 10005, Ukraine

    Valery Koval

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  1. Valery Koval
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Koval, V. A New Law of the Iterated Logarithm in Rd with Application to Matrix-Normalized Sums of Random Vectors. Journal of Theoretical Probability 15, 249–257 (2002). https://doi.org/10.1023/A:1013851720494

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