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Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors

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Abstract

We establish the strong law of large numbers with operator normalizations for vector martingales and sums of orthogonal random vectors. We describe its applications to the investigation of the strong consistency of least-squares estimators in a linear regression and the asymptotic behavior of multidimensional autoregression processes.

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Authors and Affiliations

  1. Kiev Polytechnic Institute, Kiev

    V. V. Buldygin & V. A. Koval'

Authors
  1. V. V. Buldygin
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  2. V. A. Koval'
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Buldygin, V.V., Koval', V.A. Strong Law of Large Numbers with Operator Normalizations for Martingales and Sums of Orthogonal Random Vectors. Ukrainian Mathematical Journal 52, 1195–1214 (2000). https://doi.org/10.1023/A:1010344802757

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  • DOI: https://doi.org/10.1023/A:1010344802757

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