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The law of large numbers and the Itô-Nisio theorem for vector valued random fields. (English) Zbl 0870.60006

Summary: Strong convergence results are obtained for vector-valued random fields. Substantial development of Banach-valued random fields and summability results are 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 Itô-Nisio theorem and strong laws of large numbers.

MSC:

60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)
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