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Estimation and prediction of a 2D lognormal diffusion random field
Authors:R Gutiérrez  C Roldán  R Gutiérrez-Sánchez  J M Angulo
Institution:(1) Department of Statistics and Operations Research, University of Granada, Campus Fuentenueva s/n, 18071 Granada, Spain;(2) Department of Statistics and Operations Research, University of Jaén, Paraje Las Lagunillas s/n, D-3, 23071 Jaén, Spain
Abstract:This paper describes techniques for estimation and prediction of two-parameter lognormal diffusion random fields. The drift and diffusion coefficients, which characterize a two-parameter lognormal diffusion under certain conditions, are estimated by maximum likelihood. For data on a regular grid, an alternative method is proposed to estimate the diffusion coefficient. Both of these estimates are compared in several situations. The kriging predictors are formulated involving the drift and diffusion coefficients and the predictions are obtained using the estimates of these coefficients.
Keywords:Diffusion random field  Kriging  Lognormal diffusion process
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