Scaling transition and edge effects for negatively dependent linear random fields on Z2

Donatas Surgailis

Stochastic Processes and their Applications, 2020, vol. 130, issue 12, 7518-7546

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 Z2 with moving-average coefficients a(t,s) decaying as |t|−q1 and |s|−q2 in the horizontal and vertical directions, q1−1+q2−1<1 and satisfying ∑(t,s)∈Z2a(t,s)=0. The scaling limits are taken over rectangles whose sides increase as λ and λγ when λ→∞, for any γ>0. The scaling transition occurs at γ0X>0 if the scaling limits of X are different and do not depend on γ for γ>γ0X and γ<γ0X. 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.

Date: 2020
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DOI: 10.1016/j.spa.2020.08.005

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