Probability Theory and Related Fields

, Volume 92, Issue 1, pp 91–115

Representation of linearly additive random fields

  • Toshio Mori


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∈Rd} 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∈Rd. In passing it is shown that there exists a natural one-to-one correspondence between stochastically continuous, linearly additive Poisson random fields onRd and locally finite, bundleless measures on the space of all (d-1)-hyperplanes inRd. The latter result is closely related to Ambartzumian's theorem on the representation of linearly additive pseudometrics in the plane.


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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Toshio Mori
    • 1
  1. 1.Department of MathematicsYokohama City UniversityYokohama 236Japan

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