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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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  • Valery Koval

    (Zhytomyr Institute of Engineering and Technology)

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.

Suggested Citation

  • Valery Koval, 2002. "A New Law of the Iterated Logarithm in Rd with Application to Matrix-Normalized Sums of Random Vectors," Journal of Theoretical Probability, Springer, vol. 15(1), pages 249-257, January.
    • Handle: RePEc:spr:jotpro:v:15:y:2002:i:1:d:10.1023_a:1013851720494
    DOI: 10.1023/A:1013851720494
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    References listed on IDEAS

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    1. Kaufmann, Heinz, 1987. "On the strong law of large numbers for multivariate martingales," Stochastic Processes and their Applications, Elsevier, vol. 26, pages 73-85.
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