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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 12, Issue 5


Volume 13 (2015)

On the asymptotic form of convex hulls of Gaussian random fields

Youri Davydov
  • Laboratoire Paul Painlevé, Cité Scientifique, Université Lille 1, Bâtiment M2, 59655, Villeneuve d’Ascq, France
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/ Vygantas Paulauskas
  • Department of Mathematics and Informatics, Vilnius University, Naugarduko St. 24, 03225, Vilnius, Lithuania
  • Institute of Mathematics and Informatics, Vilnius University, Akademijos St. 4, 08663, Vilnius, Lithuania
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Published Online: 2014-02-15 | DOI: https://doi.org/10.2478/s11533-013-0375-9


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.

Keywords: Gaussian processes and fields; Convex hull; Limit behavior

MSC: 62G15; 62G60; 60F15

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About the article

Published Online: 2014-02-15

Published in Print: 2014-05-01

Citation Information: Open Mathematics, Volume 12, Issue 5, Pages 711–720, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0375-9.

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