Fast and exact synthesis of some operator scaling Gaussian random fields |
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| Institution: | 1. Laboratoire de Mathématiques et Applications, UMR-CNRS 7348, Université de Poitiers, Téléport 2-BP30179, Boulevard Marie et Pierre Curie, 86962 Chasseneuil, France;2. Avignon Université, Laboratoire de Mathématiques d''Avignon (EA 2151), F-84018 Avignon, France;3. Inria, BIGS, Villers-lès-Nancy, F-54600, France;1. Leiden University, Netherlands;2. Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France;1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom;2. Department of Mathematics, University of Oslo, 0316 Oslo, Norway;1. Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway;2. Simula Research Laboratory AS, 1364 Fornebu, Norway;3. Machine Intelligence Department, Simula Metropolitan Center for Digital Engineering, 0167 Oslo, Norway;1. Department of Mathematics, Vanderbilt University, Nashville, TN, 37212, USA;2. Department of Mathematical Science, Northern Illinois University, Dekalb, IL, 60115, USA;3. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA |
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| Abstract: | Operator scaling Gaussian random fields, as anisotropic generalizations of self-similar fields, know an increasing interest for theoretical studies in the literature. However, up to now, they were only defined through stochastic integrals, without explicit covariance functions. In this paper we exhibit explicit covariance functions, as anisotropic generalizations of fractional Brownian fields ones, and define corresponding Operator scaling Gaussian random fields. This allows us to propose a fast and exact method of simulation in dimension 2 based on the circulant embedding matrix method, following ideas of Stein 34] for fractional Brownian surfaces syntheses. This is a first piece of work to popularize these models in anisotropic spatial data modeling. |
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| Keywords: | Operator scaling Self-similarity Gaussian field Fractional Brownian fields Anisotropy Covariance Simulation |
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