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- W2800180411 abstract "We provide a complete description of anisotropic scaling limits of stationary linear random field on ${mathbb {Z}}^3$ with long-range dependence and moving average coefficients decaying as $O(|t_i|^{-q_i})$ in the $i$th direction, $i=1,2,3.$ The scaling limits are taken over rectangles in ${mathbb {Z}}^3$ whose sides increase as $O(lambda^{gamma_i}), i=1,2,3$ when $lambda to infty$, for any fixed $gamma_i >0, i=1,2,3 $. We prove that all these limits are Gaussian RFs whose covariance structure essentially is determined by the fulfillment or violation of the balance conditions $gamma_i q_i = gamma_j q_j, 1 le i < j le 3$. The paper extends recent results in cite{ps2015}, cite{ps2016}, cite{pils2016}, cite{pils2017} on anisotropic scaling of long-range dependent random fields from dimension 2 to dimension 3." @default.
- W2800180411 created "2018-05-17" @default.
- W2800180411 creator A5026622957 @default.
- W2800180411 date "2018-05-09" @default.
- W2800180411 modified "2023-09-27" @default.
- W2800180411 title "Anisotropic scaling limits of long-range dependent linear random fields on ${mathbb {Z}}^3$" @default.
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