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Anisotropic scaling limits of long-range dependent random fields

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Abstract

We review recent results on anisotropic scaling limits and the scaling transition for linear and their subordinated nonlinear long-range dependent stationary random fields X on ℤ2. The scaling limits \( {V}_{\upgamma}^X \) are taken over rectangles in ℤ2 whose sides increase as O(λ) and O(λγ ) as λ→∞for any fixed γ > 0. The scaling transition occurs at \( {\upgamma}_0^X>0 \) provided that \( {V}_{\upgamma}^X \) are different for \( \upgamma >{\upgamma}_0^X \) and \( \upgamma <{\upgamma}_0^X \) and do not depend on γ otherwise.

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  1. Faculty of Mathematics and Informatics, Vilnius University, Naugarduko str. 24, LT-03225, Vilnius, Lithuania

    Donatas Surgailis

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  1. Donatas Surgailis
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Correspondence to Donatas Surgailis.

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Dedicated to Vygantas Paulauskas, my close friend since student years, who shared with me many common views about life and mathematics

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Surgailis, D. Anisotropic scaling limits of long-range dependent random fields. Lith Math J 59, 595–615 (2019). https://doi.org/10.1007/s10986-019-09459-4

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