Extremes of the standardized Gaussian noise

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Kabluchko, Zakhar

关键词: Extremes;    Gaussian fields;    Scan statistics;    Gumbel distribution;    Pickands' double-sum method;    Poisson clumping heuristics;    Local self-similarity;   

DOI  :  10.1016/j.spa.2010.11.007

来源: Elsevier

【 摘 要 】

Let {xi(k), k is an element of Z(d)) be a d-dimensional array of independent standard Gaussian random variables. For a finite set A is an element of Z(d) define S(A) = Sigma(k is an element of A) xi(k). Let vertical bar A vertical bar be the number of elements in A. We prove that the appropriately normalized maximum of S(A)/root vertical bar A vertical bar 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. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

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