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Strong Laws for Blockwise ℳ-Dependent Random Fields

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Abstract

We consider random fields and introduce a concept of ℳ-dependence for random fields. Using a lemma from summability theory we prove strong laws of large numbers for blockwise ℳ-dependent random fields under various moment conditions, thereby generalizing some results in the literature from independent random fields.

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Correspondence to Ulrich Stadtmüller.

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This research was started while the first author visited the University of Ulm, Institute of Number Theory & Probability Theory in October 2006; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046192.

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Móricz, F., Stadtmüller, U. & Thalmaier, M. Strong Laws for Blockwise ℳ-Dependent Random Fields. J Theor Probab 21, 660–671 (2008). https://doi.org/10.1007/s10959-007-0127-5

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  • DOI: https://doi.org/10.1007/s10959-007-0127-5

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