Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1154711 | Statistics & Probability Letters | 2014 | 8 Pages |
Abstract
Let {Xi(t),tâ¥0},1â¤iâ¤n be independent centered stationary Gaussian processes with unit variance and almost surely continuous sample paths. For given positive constants u,T, define the set of conjunctions C[0,T],uâ{tâ[0,T]:min1â¤iâ¤nXi(t)â¥u}. Motivated by some applications in brain mapping and digital communication systems, we obtain exact asymptotic expansion of P{C[0,T],uâ Ï}, as uââ. Moreover, we establish the Berman sojourn limit theorem for the random process {min1â¤iâ¤nXi(t),tâ¥0} and derive the tail asymptotics of the supremum of each order statistics process.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Krzysztof DÈ©bicki, Enkelejd Hashorva, Lanpeng Ji, Kamil TabiÅ,