~平稳随机场的方向幻影分布函数
Directional phantom distribution functions for~stationary random fields
摘要：
给出了正则格点上平稳随机场虚分布函数存在的充要条件。我们还介绍了一个要求较低的概念，一个方向幻影分布，具有潜在的更广泛的适用范围。这种方法导致扇形极限性质，一个众所周知的现象，在极限定理的随机场。一个平稳的高斯随机场的例子表明，这两个概念不一致。给出了极值指标和扇形极值指标的存在性判据。
英文摘要：
We give necessary and sufficient conditions for the existence of a phantom distribution function for a stationary random field on a regular lattice. We also introduce a less demanding notion of a directional phantom distribution, with potentially broader area of applicability. Such approach leads to sectorial limit properties, a phenomenon well-known in limit theorems for random fields. An example of a stationary Gaussian random field is provided showing that the two notions do not coincide. Criteria for the existence of the corresponding notions of the extremal index and the sectorial extremal index are also given.
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