Abstract
Let X={X(t),t∈T} be a non-centered, unit-variance, smooth Gaussian random field indexed on some parameter space T, and let Au(X,T)={t∈T:X(t)≥u} be the excursion set. It is shown that, as u→∞, the excursion probability ℙ{supt∈TX(t)≥u} can be approximated by the expected Euler characteristic of Au(X,T), denoted by E{χ(Au(X,T))}, such that the error is super-exponentially small. The explicit formulae for E{χ(Au(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.
Original language | English (US) |
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Pages (from-to) | 883-905 |
Number of pages | 23 |
Journal | Stochastic Processes and their Applications |
Volume | 126 |
Issue number | 3 |
DOIs | |
State | Published - Mar 2016 |
Externally published | Yes |
Keywords
- Euler characteristic
- Excursion probability
- Gaussian random fields
- Rectangle
- Sphere
- Super-exponentially small
ASJC Scopus subject areas
- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics