Excursion probability of certain non-centered smooth Gaussian random fields

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Cheng, Dan¹ 

[1] N Carolina State Univ, Dept Stat, 2311 Stinson Dr,Campus Box 8203, Raleigh, NC 27695 USA

关键词: Excursion probability;    Gaussian random fields;    Euler characteristic;    Rectangle;    Sphere;    Super-exponentially small;   

DOI  :  10.1016/j.spa.2015.10.003

来源: Elsevier

【 摘 要 】

Let X = {X (t), t is an element of T} be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space T, and let A(u)(X, T) = {t is an element of T : X(t) >= u} be the excursion set. It is shown that, as u -> infinity, the excursion probability P{sup(t is an element of T) X (t) >= u} can be approximated by the expected Euler characteristic of A(u)(X, T), denoted by Efx (Au (X, T))}, such that the error is super-exponentially small. The explicit formulae for E{x (A(u) (X, T))} are also derived for two cases: (i) T is a rectangle and X - EX is stationary; (ii) T is an N-dimensional sphere and X EX is isotropic. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

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