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On convex hull of Gaussian samples | | Yu. Davydov
; | | Date: |
27 Apr 2010 | | Abstract: | 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 $$ lim_{n o infty} frac{1}{sqrt{2ln
n}} W_n = W $$ (in the sense of Hausdorff distance), where the limit shape $W$
is defined by the covariance structure of $X$: $W = conv {}{K_t, tin T},
K_t$ 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. | | Source: | arXiv, 1004.4908 | | Services: | Forum | Review | PDF | Favorites | |
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