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Representation of linearly additive random fields
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  • Published: March 1992

Representation of linearly additive random fields

  • Toshio Mori1 

Probability Theory and Related Fields volume 92, pages 91–115 (1992)Cite this article

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Summary

Chentsov type representation theorem is proved for stochastically continuous, linearly additive, infinitely divisible random field without Gaussian component, where a random fieldX={X(t), t∈R d } is called linearly additive if the stochastic process ξ defined by ξ(λ)=X(a+λb), λ∈R, has independent increments for every pair(a, b), a, b∈R d. In passing it is shown that there exists a natural one-to-one correspondence between stochastically continuous, linearly additive Poisson random fields onR d and locally finite, bundleless measures on the space of all (d-1)-hyperplanes inR d. The latter result is closely related to Ambartzumian's theorem on the representation of linearly additive pseudometrics in the plane.

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Authors and Affiliations

  1. Department of Mathematics, Yokohama City University, 22-2 Seto, Kanazawa-ku, Yokohama 236, Japan

    Toshio Mori

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  1. Toshio Mori
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Mori, T. Representation of linearly additive random fields. Probab. Th. Rel. Fields 92, 91–115 (1992). https://doi.org/10.1007/BF01205238

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  • Received: 07 November 1990

  • Revised: 01 October 1991

  • Issue Date: March 1992

  • DOI: https://doi.org/10.1007/BF01205238

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Keywords

  • Stochastic Process
  • Probability Theory
  • Random Field
  • Mathematical Biology
  • Representation Theorem
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