Electronic Journal of Probability

Spectral conditions for equivalence of Gaussian random fields with stationary increments

Abolfazl Safikhani and Yimin Xiao

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Abstract

This paper studies the problem of equivalence of Gaussian measures induced by Gaussian random fields (GRFs) with stationary increments and proves a sufficient condition for the equivalence in terms of the behavior of the spectral measures at infinity. The main results extend those of Stein (2004), Van Zanten (2007, 2008) and are applicable to a rich family of nonstationary space-time models with possible anisotropy behavior.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 8, 19 pp.

Dates
Received: 21 July 2018
Accepted: 22 January 2019
First available in Project Euclid: 15 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1550199786

Digital Object Identifier
doi:10.1214/19-EJP270

Mathematical Reviews number (MathSciNet)
MR3916328

Zentralblatt MATH identifier
1412.60074

Subjects
Primary: 60G60: Random fields
Secondary: 62H11: Directional data; spatial statistics

Keywords
Gaussian random fields equivalence of measures nonstationary spectral density spatio-temporal models

Rights
Creative Commons Attribution 4.0 International License.

Citation

Safikhani, Abolfazl; Xiao, Yimin. Spectral conditions for equivalence of Gaussian random fields with stationary increments. Electron. J. Probab. 24 (2019), paper no. 8, 19 pp. doi:10.1214/19-EJP270. https://projecteuclid.org/euclid.ejp/1550199786


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