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I just want to know what kind of phenomenon a integrated gaussian process ($Y_{t}=\int_{0}^{t}X_{s}ds$ where X is a gaussian process) can modelize. Thanks.

kacou
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1 Answers1

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Gaussian process has been a popular model in geostatistics. It is commonly used to model the spatial distribution of the ore grade. Let $Z(x,y)$ be a 2D gaussian process that represent the ore grade obtained from the sample at location $(x,y)$. Then $Y_\Omega=\int_\Omega Z(x,y)dxdy$ gives the total amount of ore in the region $\Omega$.

(Refer to Cressie, N. (1991). Statistics for spatial data. John Wiley & Sons. Page 106, Block average section)

Andi Wang
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  • Does the index set of a Gaussian ( or general random) process have an ordering to it, at least a partial ordering, so that we can compare at least some $X_t, X_j$ , to have $t<j$? Also, I don't see in the integral where the index set is used? – gary Sep 06 '18 at 21:20