Abstract
This paper describes techniques for estimation, prediction and conditional simulation of two-parameter lognormal diffusion random fields which are diffusions on each coordinate and satisfy a particular Markov property. The estimates of the drift and diffusion coefficients, which characterize the lognormal diffusion random field under certain conditions, are used for obtaining kriging predictors. The conditional simulations are obtained using the estimates of the drift and diffusion coefficients, kriging prediction and unconditional simulation for the lognormal diffusion random field.
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References
G. Christakos, Random Field Models in Earth Sciences, Academic: San Diego, 1992.
N. Cressie, Statistics for Spatial Data, Wiley: New York, 1993 (rev. ed.).
R. Gutiérrez, C. Roldán, R. Gutiérrez-Sánchez, and J. M. Angulo, “Estimation and prediction of a 2D lognormal diffusion random field,” Stochastic Environmental Research and Risk Assessment vol. 19(4) pp. 258–265, 2005.
D. Nualart, “Two-parameter diffusion processes and martingales,” Stochastic Processes and Their Applications vol. 15 pp. 31–57, 1983.
L. Yuh-Ming and J. Hugh Ellis, “Estimation and simulation of lognormal random fields,” Computers and Geosciences vol. 23(1) pp. 19–31, 1997.
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Gutiérrez, R., Roldán, C., Gutiérrez-Sánchez, R. et al. Prediction and Conditional Simulation of a 2D Lognormal Diffusion Random Field. Methodol Comput Appl Probab 9, 413–423 (2007). https://doi.org/10.1007/s11009-007-9029-3
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DOI: https://doi.org/10.1007/s11009-007-9029-3