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The Law of Large Numbers and the Ito-Nisio Theorem for Vector Valued Random Fields |
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| Authors: | J Hoffmann-Jørgensen K-L Su R L Taylor |
| Institution: | (1) Matematisk Institut, Aarhus Universitet, Ny Munkegade, DK-8000 Aarhus, Denmark;(2) Department of Business, National Open University, Taichang, Taiwan, Republic of China;(3) Department of Statistics, University of Georgia, Athens, Georgia, 30602-1952 |
| 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. |
| Keywords: | Random field Banach space law of large numbers |
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