On the asymptotic form of convex hulls of Gaussian random fields

• Autorzy: Youri Davydov , Vygantas Paulauskas
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Gaussian processes and fields; Convex hull; Limit behavior

Kategorie tematyczne

• 60F15: Strong theorems
• 62G15: Tolerance and confidence regions

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 5
• Strony: 711-720

Daty

wydano

2014-05-01

online

2014-02-15

Twórcy

autor

Youri Davydov

• Université Lille 1

autor

Vygantas Paulauskas

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0375-9