A Fourier-RKHS approach for characterizing equivalent Gaussian distributions for stationary processes on homogeneous spaces

2025/12/23 by Hediger, Michael
#43A90 #46E22 #60G10 #60G15 #60G30 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2512.20248

Abstract

Pairs of equivalent Gaussian distributions for centered stationary processes on homogeneous spaces can be characterized in terms of their spectral measures. The purpose of this note is to consider the latter characterization from the perspective of a reproducing kernel Hilbert space (RKHS) approach.

Citations

• Inference for Gaussian Processes with Matérn Covariogram on Compact Riemannian Manifolds
• Asymptotic analysis of maximum likelihood estimation of covariance parameters for Gaussian processes: an introduction with proofs
• Estimation and Prediction using generalized Wendland Covariance Functions under fixed domain asymptotics
• On the consistent separation of scale and variance for Gaussian random fields
• Maximum likelihood estimation of models for residual covariance in spatial regression

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