Abstract
In 1984, C. M. Newman posed the problem of proving the invariance principle in distribution for associated random fields (i. e., fields satisfying the so-called FKG-inequalities)X={Xj, j∈Zd} when d≥3. The solution of this problem for wide-sense stationary associated random fields is obtained here under slightly more restrictive conditions than those used by C. M. Newman and A. L. Wright for the strictly stationary case where d=1 and d=2.
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Partially supported by the Russian Foundation for Fundamental Research (grant No. 93-01-01454).
Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part I.
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Bulinski, A.V., Keane, M.S. Invariance principle for associated random fields. J Math Sci 81, 2905–2911 (1996). https://doi.org/10.1007/BF02362501
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DOI: https://doi.org/10.1007/BF02362501