Equivalence between Kriging and CPDF Methods for Conditional Simulation

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Abstract
Currently the kriging and conditional probability density function (CPDF) methods are widely used in solving the conditional simulation problems involving stochastic processes and fields. For the fundamental understanding of these two methods, this paper considers their applications to the conditional simulation of a one-dimensional, univariate and stationary stochastic process or field. The major findings of this study are as follows. First, the two methods are completely equivalent if the stochastic process is Gaussian with a zero mean. Specifically, the best linear unbiased estimate (BLUE) and the kriging variance are identical to the corresponding conditional mean and variance, respectively. Second, when the kriging method is used, the conditional simulation of a nonzero mean stochastic process (with a known value of the mean) is not equivalent to the (nonzero) mean plus the conditional simulation of the zero mean stochastic process obtained by subtracting the nonzero mean from the original process. T...

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