ON CONVEX HULL OF GAUSSIAN SAMPLES

被引:6
作者
Davydov, Youri [1 ]
机构
[1] Univ Lille 1, F-59655 Villeneuve Dascq, France
关键词
Gaussian process; Gaussian sample; convex hull; limit theorem;
D O I
10.1007/s10986-011-9117-5
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let X-i = {X-i(t), t is an element of T} be i. i. d. copies of a centered Gaussian process X = {X(t), t is an element of T} with values in R-d defined on a separable metric space T. It is supposed that X is bounded. We consider the asymptotic behavior of convex hulls W-n = conv{X-1(t),..., X-n(t), t is an element of T} and show that, with probability 1, lim n ->infinity 1/root 2ln nW(n) = W (in the sense of Hausdorff distance), where the limit shape W is defined by the covariance structure of X: W = conv{K-t, t is an element of T}, K-t being the concentration ellipsoid of X(t). We also study the asymptotic behavior of the mathematical expectations Ef(W-n), where f is an homogeneous functional.
引用
收藏
页码:171 / 179
页数:9
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