Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7549618 | Statistics & Probability Letters | 2014 | 4 Pages |
Abstract
For a centered Gaussian random field X={X(t),tâRN}, let T1 and T2 be two compact sets in RN such that I=T1â©T2â 0̸ and denote by Ï(Au(I)) the Euler characteristic of the excursion set Au(I)={tâI:X(t)â¥u}. We show that under certain smoothness and regularity conditions, as uââ, the joint excursion probability P{suptâT1X(t)â¥u,supsâT2X(s)â¥u} can be approximated by the expected Euler characteristic E{Ï(Au(I))} such that the error is super-exponentially small.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Dan Cheng,