On the asymptotic form of convex hulls of Gaussian random fields

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On the asymptotic form of convex hulls of Gaussian random fields. / Davydov, Youri; Paulauskas, Vygantas.

In: Central European Journal of Mathematics, Vol. 12, No. 5, 05.2014, p. 711-720.

Research output: Contribution to journal › Article › peer-review

Author

Davydov, Youri ; Paulauskas, Vygantas. / On the asymptotic form of convex hulls of Gaussian random fields. In: Central European Journal of Mathematics. 2014 ; Vol. 12, No. 5. pp. 711-720.

BibTeX

@article{f42b630300294dd0ba3c13d7794ce2fc,

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

abstract = "We consider a centered Gaussian random field X = {X t: t ∈ T} with values in a Banach space B defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution P 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, (Formula presented.) (in the sense of Hausdorff distance), where the limit set [InlineMediaObject not available: see fulltext.] is the concentration ellipsoid of P. The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.",

keywords = "Convex hull, Gaussian processes and fields, Limit behavior",

author = "Youri Davydov and Vygantas Paulauskas",

year = "2014",

month = may,

doi = "10.2478/s11533-013-0375-9",

language = "English",

volume = "12",

pages = "711--720",

journal = "Open Mathematics",

issn = "1895-1074",

publisher = "Versita",

number = "5",

}

RIS

TY - JOUR

T1 - On the asymptotic form of convex hulls of Gaussian random fields

AU - Davydov, Youri

AU - Paulauskas, Vygantas

PY - 2014/5

Y1 - 2014/5

N2 - We consider a centered Gaussian random field X = {X t: t ∈ T} with values in a Banach space B defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution P 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, (Formula presented.) (in the sense of Hausdorff distance), where the limit set [InlineMediaObject not available: see fulltext.] is the concentration ellipsoid of P. The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.

AB - We consider a centered Gaussian random field X = {X t: t ∈ T} with values in a Banach space B defined on a parametric set T equal to ℝm or ℤm. It is supposed that the distribution P 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, (Formula presented.) (in the sense of Hausdorff distance), where the limit set [InlineMediaObject not available: see fulltext.] is the concentration ellipsoid of P. The asymptotic behavior of the mathematical expectations Ef(W n), where f is some function, is also studied.

KW - Convex hull

KW - Gaussian processes and fields

KW - Limit behavior

UR - http://www.scopus.com/inward/record.url?scp=84893924427&partnerID=8YFLogxK

U2 - 10.2478/s11533-013-0375-9

DO - 10.2478/s11533-013-0375-9

M3 - Article

AN - SCOPUS:84893924427

VL - 12

SP - 711

EP - 720

JO - Open Mathematics

JF - Open Mathematics

SN - 1895-1074

IS - 5

ER -

ID: 73459914