Equivalence of Gaussian measures of multivariate random fields

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• 作者：M. D. Ruiz-Medina (1)
  E. Porcu (2)
  
  1. Department of Statistics and Operations Research ; Faculty of Sciences ; University of Granada ; Campus Fuente Nueva s/n ; 18071 ; Granada ; Spain
  2. Department of Mathematics ; University Federico Santa Maria ; Avenida Espaa ; Valparaiso ; Chile
  
• 关键词：Equivalence of Gaussian measures ; Hilbert ; valued vector random variables ; Multivariate Gaussian random fields ; Multivariate infinite ; dimensional Gaussian measures ; Trace covariance operators ; Tapering
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：29
• 期：2
• 页码：325-334
• 全文大小：337 KB
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• 刊物类别：Earth and Environmental Science
• 刊物主题：Environment
  Mathematical Applications in Environmental Science
  Mathematical Applications in Geosciences
  Probability Theory and Stochastic Processes
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Numerical and Computational Methods in Engineering
  Waste Water Technology, Water Pollution Control, Water Management and Aquatic Pollution
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-3259

文摘

Problems related to weather forecast, forest attributes estimation and prediction, disease propagation, among others, are commonly approximated in the framework of multivariate Gaussian random field modeling. This paper deals with the equivalence condition of two zero-mean Gaussian infinite-dimensional vector measures defined on the finite product of separable Hilbert spaces. In particular, sufficient conditions are provided. The results derived are applied to obtain the equivalence of Gaussian measures associated with two stationary zero-mean Gaussian vector random fields. Classical problems related to, for example, asymptotic properties of maximum likelihood vector Gaussian random field parameter estimators from tapered multivariate covariance functions, often arising in Multivariate Geostatistics, can be solved as direct application of the results derived.