Regularly varying random fields |
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| Institution: | 1. Department of Electrical Engineering, Columbia University, New York, NY 10027, United States;2. Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027, United States |
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| Abstract: | We study the extremes of multivariate regularly varying random fields. The crucial tools in our study are the tail field and the spectral field, notions that extend the tail and spectral processes of Basrak and Segers (2009). The spatial context requires multiple notions of extremal index, and the tail and spectral fields are applied to clarify these notions and other aspects of extremal clusters. An important application of the techniques we develop is to the Brown–Resnick random fields. |
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| Keywords: | Regular variation Random field Tail field Spectral field Extremal index Brown–Resnick random field |
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