# On the asymptotic form of convex hulls of Gaussian random fields

Youri Davydov; Vygantas Paulauskas

Open Mathematics (2014)

- Volume: 12, Issue: 5, page 711-720
- ISSN: 2391-5455

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topYouri Davydov, and Vygantas Paulauskas. "On the asymptotic form of convex hulls of Gaussian random fields." Open Mathematics 12.5 (2014): 711-720. <http://eudml.org/doc/269078>.

@article{YouriDavydov2014,

abstract = {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 = convX 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.},

author = {Youri Davydov, Vygantas Paulauskas},

journal = {Open Mathematics},

keywords = {Gaussian processes and fields; Convex hull; Limit behavior; convex hull; limit behavior},

language = {eng},

number = {5},

pages = {711-720},

title = {On the asymptotic form of convex hulls of Gaussian random fields},

url = {http://eudml.org/doc/269078},

volume = {12},

year = {2014},

}

TY - JOUR

AU - Youri Davydov

AU - Vygantas Paulauskas

TI - On the asymptotic form of convex hulls of Gaussian random fields

JO - Open Mathematics

PY - 2014

VL - 12

IS - 5

SP - 711

EP - 720

AB - 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 = convX 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.

LA - eng

KW - Gaussian processes and fields; Convex hull; Limit behavior; convex hull; limit behavior

UR - http://eudml.org/doc/269078

ER -

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