Extremes of the standardized Gaussian noise

Let be a d-dimensional array of independent standard Gaussian random variables. For a finite set define . Let A be the number of elements in A. We prove that the appropriately normalized maximum of , where A ranges over all discrete cubes or rectangles contained in {1,...,n}d, converges in law to the Gumbel extreme-value distribution as n-->[infinity]. We also prove a continuous-time counterpart of this result.

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Year of publication:	2011
Authors:	Kabluchko, Zakhar
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 3, p. 515-533
Publisher:	Elsevier
Keywords:	Extremes Gaussian fields Scan statistics Gumbel distribution Pickands' double-sum method Poisson clumping heuristics Local self-similarity

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

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