Stationary Symmetric <Emphasis Type="Italic">α</Emphasis>-Stable Discrete Parameter Random Fields |
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Authors: | Parthanil Roy Gennady Samorodnitsky |
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Institution: | (1) School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA |
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Abstract: | We establish a connection between the structure of a stationary symmetric α-stable random field (0<α<2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosiński (Ann. Probab. 28:1797–1813,
2000). With the help of this connection, we study the extreme values of the field over increasing boxes. Depending on the ergodic
theoretical and group theoretical structures of the underlying action, we observe different kinds of asymptotic behavior of
this sequence of extreme values.
Supported in part by NSF grant DMS-0303493, NSA grant MSPF-05G-049 and NSF training grant “Graduate and Postdoctoral Training
in Probability and Its Applications” at Cornell University. |
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Keywords: | 60G60 37A40 |
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