Abstract
Extremal behavior of stationary Gaussian sequences/random fields is widely investigated since it models common cluster phenomena and brings a bridge between discrete and continuous extremes. We establish extensively limit theorems of stationary random fields under certain mixing and dependence conditions, which are further illustrated by typical examples of order statistics of Gaussian random fields and skew-Gaussian random fields. The positivity of the cluster index involved and its link with the expected cluster size are discussed.
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Acknowledgements
We are grateful to the referees and the Editors for their numerous suggestions and comments which corrected some mistakes and improved greatly the paper. The author would like to thank Enkelejd Hashorva for several useful discussions and important comments during the work of the contribution. The National Natural Science Foundation of China (11604375) is acknowledged.
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Ling, C. Extremes of stationary random fields on a lattice. Extremes 22, 391–411 (2019). https://doi.org/10.1007/s10687-019-00349-z
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DOI: https://doi.org/10.1007/s10687-019-00349-z
Keywords
- Stationary random fields
- Clusters index
- Mixing conditions
- Order statistics of Gaussian random fields
- Skew-Gaussian random fields