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The statistics of weighted Voronoi tessellation with a Poisson field of centroids: The estimation of the volume composition

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Abstract

In a linear section of a weighted Voronoi tessellation, with a Poisson field of centroids, a Markov process is considered, from the properties of which there follows the consistency of the linear estimate of the volume composition. The terms of the covariance matrix of the composition are estimated from above.

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Literature cited

  1. 1.

    B. P. Kharlamov, “Weighted Voronoi tessellation with a Poisson field of centroids,” Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst.,153, 160–172 (1986).

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 166, pp. 167–178, 1988.

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Kharlamov, B.P. The statistics of weighted Voronoi tessellation with a Poisson field of centroids: The estimation of the volume composition. J Math Sci 52, 2983–2991 (1990). https://doi.org/10.1007/BF01103757

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Keywords

  • Covariance
  • Covariance Matrix
  • Markov Process
  • Linear Estimate
  • Linear Section