an:07179518
Zbl 1456.60123
Surgailis, Donatas
Anisotropic scaling limits of long-range dependent random fields
EN
Lith. Math. J. 59, No. 4, 595-615 (2019).
00445259
2019
j
60G60 60G15 60G18 60G22
long-range dependent random fields; anisotropic scaling limits
Summary: 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 \(\mathbb{Z}^2\). The scaling limits \({V}_{\gamma}^X\) are taken over rectangles in \(\mathbb{Z}^2\) whose sides increase as \(O( \lambda )\) and \(O(\lambda \gamma \) ) as \(\lambda \rightarrow \infty\) for any fixed \(\gamma > 0\). The scaling transition occurs at \({\gamma}_0^X>0\) provided that \({V}_{\gamma}^X\) are different for \(\gamma >{\gamma}_0^X\) and \(\gamma <{\gamma}_0^X\) and do not depend on \(\gamma\) otherwise.