Stationary covariances associated with exponentially convex functions

Werner Ehm; Marc G. Genton; Tilmann Gneiting

doi:10.3150/bj/1066223271

Stationary covariances associated with exponentially convex functions

Werner Ehm^*, Marc G. Genton, Tilmann Gneiting

^*Corresponding author for this work

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

35 Scopus citations

Abstract

We establish a bijection between exponentially convex functions and entire positive definite functions, and extend Loève's construction of stochastic processes associated with them. As an application, we derive parametric covariance models for locally stationary random fields.

Original language	English (US)
Pages (from-to)	607-615
Number of pages	9
Journal	Bernoulli
Volume	9
Issue number	4
DOIs	https://doi.org/10.3150/bj/1066223271
State	Published - Aug 2003
Externally published	Yes

Keywords

Characteristic function
Exponential family
Exponentially convex
Laplace transform
Locally stationary
Positive definite
Random field

ASJC Scopus subject areas

Statistics and Probability

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10.3150/bj/1066223271

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title = "Stationary covariances associated with exponentially convex functions",

abstract = "We establish a bijection between exponentially convex functions and entire positive definite functions, and extend Lo{\`e}ve's construction of stochastic processes associated with them. As an application, we derive parametric covariance models for locally stationary random fields.",

keywords = "Characteristic function, Exponential family, Exponentially convex, Laplace transform, Locally stationary, Positive definite, Random field",

author = "Werner Ehm and Genton, {Marc G.} and Tilmann Gneiting",

year = "2003",

month = aug,

doi = "10.3150/bj/1066223271",

language = "English (US)",

volume = "9",

pages = "607--615",

journal = "Bernoulli",

issn = "1350-7265",

publisher = "Bernoulli Society for Mathematical Statistics and Probability",

number = "4",

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TY - JOUR

T1 - Stationary covariances associated with exponentially convex functions

AU - Ehm, Werner

AU - Genton, Marc G.

AU - Gneiting, Tilmann

PY - 2003/8

Y1 - 2003/8

N2 - We establish a bijection between exponentially convex functions and entire positive definite functions, and extend Loève's construction of stochastic processes associated with them. As an application, we derive parametric covariance models for locally stationary random fields.

AB - We establish a bijection between exponentially convex functions and entire positive definite functions, and extend Loève's construction of stochastic processes associated with them. As an application, we derive parametric covariance models for locally stationary random fields.

KW - Characteristic function

KW - Exponential family

KW - Exponentially convex

KW - Laplace transform

KW - Locally stationary

KW - Positive definite

KW - Random field

UR - http://www.scopus.com/inward/record.url?scp=2442634820&partnerID=8YFLogxK

U2 - 10.3150/bj/1066223271

DO - 10.3150/bj/1066223271

M3 - Article

AN - SCOPUS:2442634820

SN - 1350-7265

VL - 9

SP - 607

EP - 615

JO - Bernoulli

JF - Bernoulli

IS - 4

ER -

Stationary covariances associated with exponentially convex functions

Abstract

Keywords

ASJC Scopus subject areas

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