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The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields

Author

Listed:
  • J. Hoffmann-Jørgensen

    (Aarhus Universitet)

  • K-L. Su

    (National Open University)

  • R. L. Taylor

    (University of Georgia)

Abstract

Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results is needed to provide the framework for the major results since many plausible extensions fail for multi-indexed Banach-valued random variables. This development yields general convergence results for random fields in Banach spaces, including an Ito-Nisio theorem and strong laws of large numbers.

Suggested Citation

  • J. Hoffmann-Jørgensen & K-L. Su & R. L. Taylor, 1997. "The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields," Journal of Theoretical Probability, Springer, vol. 10(1), pages 145-183, January.
    • Handle: RePEc:spr:jotpro:v:10:y:1997:i:1:d:10.1023_a:1022650616646
    DOI: 10.1023/A:1022650616646
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    References listed on IDEAS

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    1. Andre Adler & Andrew Rosalsky & Robert L. Taylor, 1989. "Strong laws of large numbers for weighted sums of random elements in normed linear spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 12, pages 1-23, January.
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