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- W3162093121 abstract "We obtain a complete description of local anisotropic scaling limits for a class of fractional random fields $X$ on ${mathbb{R}}^2$ written as stochastic integral with respect to infinitely divisible random measure. The scaling procedure involves increments of $X$ over points the distance between which in the horizontal and vertical directions shrinks as $O(lambda)$ and $O(lambda^gamma)$ respectively as $lambda downarrow 0$, for some $gamma>0$. We consider two types of increments of $X$: usual increment and rectangular increment, leading to the respective concepts of $gamma$-tangent and $gamma$-rectangent random fields. We prove that for above $X$ both types of local scaling limits exist for any $gamma>0$ and undergo a transition, being independent of $gamma>gamma_0$ and $gamma<gamma_0$, for some $gamma_0>0$; moreover, the unbalanced scaling limits ($gammanegamma_0$) are $(H_1,H_2)$-multi self-similar with one of $H_i$, $i=1,2$, equal to $0$ or $1$. The paper extends Pilipauskait.e and Surgailis (2017) and Surgailis (2020) on large-scale anisotropic scaling of random fields on ${mathbb{Z}}^2$ and Benassi et al. (2004) on $1$-tangent limits of isotropic fractional L'evy random fields." @default.
- W3162093121 created "2021-05-24" @default.
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- W3162093121 date "2022-11-01" @default.
- W3162093121 modified "2023-10-05" @default.
- W3162093121 title "Local scaling limits of Lévy driven fractional random fields" @default.
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- W3162093121 doi "https://doi.org/10.3150/21-bej1439" @default.
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