长程相关高斯随机场的标度跃迁
Scaling transition for long-range dependent Gaussian random fields
摘要：
在Puplinskaite和Surgailis（2014）中，我们引入了$\mathbb{Z}^2$上的平稳随机场$X$的标度转换的概念，即边以可能不同的速率增长的矩形上的$X$的部分和极限或标度极限。本文证明了一类自然的具有长程相关的平稳高斯随机场在$\mathbb{Z}^2$上的标度跃迁的存在性。这种随机场的标度极限的识别和特征的依赖性质的矩形增量。
英文摘要：
In Puplinskaite and Surgailis (2014) we introduced the notion of scaling transition for stationary random fields $X$ on $\mathbb{Z}^2$ in terms of partial sums limits, or scaling limits, of $X$ over rectangles whose sides grow at possibly different rate. The present paper establishes the existence of scaling transition for a natural class of stationary Gaussian random fields on $\mathbb{Z}^2$ with long-range dependence. The scaling limits of such random fields are identified and characterized by dependence properties of rectangular increments.
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