Annals of Statistics

Some asymptotic results of Gaussian random fields with varying mean functions and the associated processes

Jingchen Liu and Gongjun Xu

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In this paper, we derive tail approximations of integrals of exponential functions of Gaussian random fields with varying mean functions and approximations of the associated point processes. This study is motivated naturally by multiple applications such as hypothesis testing for spatial models and financial applications.

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Ann. Statist., Volume 40, Number 1 (2012), 262-293.

First available in Project Euclid: 29 March 2012

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Primary: 60G15: Gaussian processes 65C05: Monte Carlo methods

Gaussian process integral change of measure


Liu, Jingchen; Xu, Gongjun. Some asymptotic results of Gaussian random fields with varying mean functions and the associated processes. Ann. Statist. 40 (2012), no. 1, 262--293. doi:10.1214/11-AOS960.

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Supplemental materials

  • Supplementary material: Proofs of several lemmas in Section 5 and the numerical results. This supplement contains proofs of Lemmas 5.2, 5.4, 5.5, 5.8 and 5.9 as well as numerical results.