On convex hull of Gaussian samples

Details On convex hull of Gaussian samples On convex hull of Gaussian samples

2010-04-27

arxiv.org/abs/1004.4908v1

Mathematics

Probability

10 pages

Scientific paper

Let $X_i = {X_i(t), t \in T}$ be i.i.d. copies of a centered Gaussian process $X = {X(t), t \in T}$ with values in $\mathbb{R}^d$ defined on a separable metric space $T.$ It is supposed that $X$ is bounded. We consider the asymptotic behaviour of convex hulls $$ W_n = \conv\ {X_1(t), X_n(t), t \in T}$$ and show that with probability 1 $$ \lim_{n\to \infty} \frac{1}{\sqrt{2\ln n}} W_n = W $$ (in the sense of Hausdorff distance), where the limit shape $W$ is defined by the covariance structure of $X$: $W = \conv {}\{K_t, t\in T}, K_t$ being the concentration ellipsoid of $X(t).$ The asymptotic behavior of the mathematical expectations $Ef(W_n)$, where $f$ is an homogeneous functional is also studied.

Affiliated with

Also associated with

No associations

Rating

On convex hull of Gaussian samples does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On convex hull of Gaussian samples, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On convex hull of Gaussian samples will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-67399