Abstract We obtain a complete description of anisotropic scaling limits and the existence of scaling transition for a class of negatively dependent linear random fields X on Z 2 with moving-average coefficients a ( t , s ) decaying as | t | − q 1 and | s | − q 2 in the horizontal and vertical directions, q 1 − 1 + q 2 − 1 1 and satisfying ∑ ( t , s ) ∈ Z 2 a ( t , s ) = 0 . The scaling limits are taken over rectangles whose sides increase as λ and λ γ when λ → ∞ , for any γ > 0 . The scaling transition occurs at γ 0 X > 0 if the scaling limits of X are different and do not depend on γ for γ > γ 0 X and γ γ 0 X . We prove that the scaling transition in this model is closely related to the presence or absence of the edge effects. The paper extends the results in Pilipauskaitė and Surgailis (2017) on the scaling transition for a related class of random fields with long-range dependence.

中文翻译：

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Z2 上负相关线性随机场的缩放过渡和边缘效应

摘要 我们获得了对 Z 2 上一类负相关线性随机场 X 的各向异性标度限制和标度转换存在的完整描述，其中移动平均系数 a ( t , s ) 衰减为 | 吨| − q 1 和 | | − q 2 在水平和垂直方向上，q 1 − 1 + q 2 − 1 1 并且满足∑ ( t , s ) ∈ Z 2 a ( t , s ) = 0 。对于任何 γ > 0 ，当 λ → ∞ 时，对边增加为 λ 和 λ γ 的矩形采用缩放限制。如果 X 的缩放限制不同并且不依赖于 γ γ > γ 0 X 和 γ γ 0 X ，则缩放转换发生在 γ 0 X > 0 处。我们证明该模型中的缩放转换与边缘效应的存在或不存在密切相关。