Asymptotic behaviour of Gaussian random fields

Joaquin Ortega

doi:10.1007/BF00531741

Asymptotic behaviour of Gaussian random fields

Joaquin Ortega

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Abstract

Let X={X(t), t∈ℝN} be a centred Gaussian random field with covariance ℰX(t)X(s)=r(t-s) continuous on ℝN×ℝN and r(0)=1. Let σ(t,s)=(ℰ(X(t)-X(s))2)1/2; σ(t,s) is a pseudometric on ℝN. Assume X is σ-separable. Let D1 be the unit cube in ℝN and for 0

Original language	English (US)
Journal	Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
Volume	59
Issue number	2
DOIs	https://doi.org/10.1007/BF00531741
State	Published - Jun 1 1982
Externally published	Yes

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N2 - Let X={X(t), t∈ℝN} be a centred Gaussian random field with covariance ℰX(t)X(s)=r(t-s) continuous on ℝN×ℝN and r(0)=1. Let σ(t,s)=(ℰ(X(t)-X(s))2)1/2; σ(t,s) is a pseudometric on ℝN. Assume X is σ-separable. Let D1 be the unit cube in ℝN and for 0

AB - Let X={X(t), t∈ℝN} be a centred Gaussian random field with covariance ℰX(t)X(s)=r(t-s) continuous on ℝN×ℝN and r(0)=1. Let σ(t,s)=(ℰ(X(t)-X(s))2)1/2; σ(t,s) is a pseudometric on ℝN. Assume X is σ-separable. Let D1 be the unit cube in ℝN and for 0

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M3 - Article

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JF - Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete

IS - 2

ER -

Asymptotic behaviour of Gaussian random fields

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