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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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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DOI: https://doi.org/10.1007/BF01205238
Keywords
- Stochastic Process
- Probability Theory
- Random Field
- Mathematical Biology
- Representation Theorem