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Asymptotical behaviour for some functionals of positively and negatively dependent random fields. (Russian. English summary) Zbl 0968.60044
The authors estimate the difference between the values taken by certain functionals on weighted partial sums type and on suitable Gaussian processes. The former processes arise from random fields indexed on $$\mathbb{Z}^d$$, $$d\geq 1$$, which are either weakly associated or negatively dependent. The authors’ approach leans on works of A. D. Barbour [Probab. Theory Relat. Fields 84, No. 3, 297-322 (1990; Zbl 0665.60008)], F. Götze [Ann. Probab. 19, No. 2, 724-739 (1991; Zbl 0729.62051)], and C. Stein [in: Proc. 6th Berkeley Sympos. Math. Statist. Probab. 2, 583-602 (1972; Zbl 0278.60026)].

##### MSC:
 60G60 Random fields 60E15 Inequalities; stochastic orderings
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