Geodesic
Statistics of the weighted Voronoi partition with the Poisson field of centers: Estimation of the volume content
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 167-178

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The Markov process is considered in the line section of the weighted Voronoi tesselation with a Poisson center field. Consistency of the linear estimation of the volume ratio follows from its properties. Members of the covariance matrix of the ratio are estimated from above. 
@article{ZNSL_1988_166_a19,
     author = {B. P. Harlamov},
     title = {Statistics of the weighted {Voronoi} partition with the {Poisson} field of centers: {Estimation} of the volume content},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--178},
     publisher = {mathdoc},
     volume = {166},
     year = {1988},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a19/}
}
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B. P. Harlamov. Statistics of the weighted Voronoi partition with the Poisson field of centers: Estimation of the volume content. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part 8, Tome 166 (1988), pp. 167-178. http://geodesic.mathdoc.fr/item/ZNSL_1988_166_a19/