Directional phantom distribution functions for~stationary random fields

2020/04/14 by Adam Jakubowski, Jakubowski, Adam, Igor Rodionov +3
Mathematics · #60G15 #60G60 #60G70 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G15 #msc:60G60 #msc:60G70

paper · pdf · doi:10.48550/arxiv.2004.06767

24 pages, 2 figures

arxiv created 2020/04/14 · arxiv updated 2020/04/16

Abstract

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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