论文标题
$ {\ Mathbb {z}}^2 $的线性随机字段的缩放限制，带有通用依赖轴
Scaling limits of linear random fields on ${\mathbb{Z}}^2$ with general dependence axis
论文作者
论文摘要
我们讨论了$ {\ Mathbb {z}}}^2 $的远程依赖性线性随机字段$ x $的各向异性缩放尺度，具有任意依赖性轴（在平面上以最小的速率移动平均系数衰减的方向）。缩放限制是在矩形上平行于坐标轴的矩形，当$λ\ to \ infty $（对于任何$γ> 0 $）时，将其增加为$λ$和$λ^γ$。如果$ x $的比例限制不同，并且不依赖$γ>γ>γ>γ>γ^x_0 $和$γ<γ^x_0 $，则缩放过渡发生在$γ^x_0> 0 $。我们证明，“倾斜”依赖轴（或不协调的缩放）的事实极大地改变了上述模型中的缩放跃迁，以使$γ_0^x = 1 $独立于其他参数，将pilipauskaitė和surgailis（2017）的结果与一致的缩放级别转换相比。
We discuss anisotropic scaling of long-range dependent linear random fields $X$ on ${\mathbb{Z}}^2$ with arbitrary dependence axis (direction in the plane along which the moving-average coefficients decay at a smallest rate). The scaling limits are taken over rectangles whose sides are parallel to the coordinate axes and increase as $λ$ and $λ^γ$ when $λ\to \infty$, for any $γ>0$. The scaling transition occurs at $γ^X_0 >0$ if the scaling limits of $X$ are different and do not depend on $γ$ for $γ> γ^X_0 $ and $γ< γ^X_0$. We prove that the fact of `oblique' dependence axis (or incongruous scaling) dramatically changes the scaling transition in the above model so that $γ_0^X = 1$ independently of other parameters, contrasting the results in Pilipauskaitė and Surgailis (2017) on the scaling transition under congruous scaling.
