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On the asymptotic form of convex hulls of Gaussian random fields

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Davydov Y., Paulauskas V.

Open Mathematics

2014

tom 12

nr 5

711-720

We consider a centered Gaussian random field X = {X t : t ∈ T} with values in a Banach space $$\mathbb{B}$$ defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution of X t is independent of t. We consider the asymptotic behavior of closed convex hulls W n = conv{X t : t ∈ T n}, where (T n) is an increasing sequence of subsets of T. We show that under some conditions of weak dependence for the random field under consideration and some sequence (b n)n≥1 with probability 1, (in the sense of Hausdorff distance), where the limit set is the concentration ellipsoid of . The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.

Ograniczanie wyników

1 Open Mathematics

1 Davydov Y.

1 Paulauskas V.

1 2014

Wyniki wyszukiwania

On the asymptotic form of convex hulls of Gaussian random fields