Multivariate Spartan spatial random field models |
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| Affiliation: | 1. Geostatistics Research Unit, Department of Mineral Resources Engineering, Technical University of Crete, Chania 73100, Greece;2. Universidad Técnica Federico Santa Maria, Department of Mathematics, Valparaiso, Chile;1. Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35 (Agora), FI-40014, Finland;2. Institute for Problems in Mechanics RAS, Prospect Vernadskogo 101, Bld. 1, 119526 Moscow, Russian Federation;1. Faculty of Science and Technology, University of Macau, Macao, China;2. Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Hong Kong, China;1. Department of Civil, Environmental and Architectural Engineering, University of Genova, Italy;2. NatHaz Modeling Laboratory, University of Notre Dame, IN, USA;1. State Key Laboratory for Strength and Vibration of Mechanical Structures/School of Aerospace, Xi?an Jiaotong University, Xi?an 710049, China;2. School of Science, Chang?an University, Xi?an 710064, China |
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| Abstract: | This paper introduces a family of stationary multivariate spatial random fields with D scalar components that extend the scalar model of Gibbs random fields with local interactions (i.e., Spartan spatial random fields). We derive permissibility conditions for Spartan multivariate spatial random fields with a specific structure of local interactions. We also present explicit expressions for the respective matrix covariance functions obtained at the limit of infinite spectral cutoff in one, two and three spatial dimensions. Finally, we illustrate the proposed covariance models by means of simulated bivariate time series and two-dimensional random fields. |
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| Keywords: | Cramer?s theorem Stationary Multivariate spatial data Multivariate time series Simulation |
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