Summary
We define a new class of Markov random fields with two-dimensional parameter z∈T⊂ℝ2, which take a finite number of values separated by random polygonal boundaries. In some special cases, these random fields are consistent in T and allow and alternative description in terms of the equilibrium evolution of a system of one-dimensional particles.
References
Arak, T.: On Markovian random fields with finite number of values. 4th USSR-Japan symposium on probability theory and mathematical statistics. Abstracts of communications, Tbilisi 1982
Kendall, M.G., Moran, P.A.P.: Geometrical probability. New York: Hafner 1963
Rozanov, Ju.A.: Markov random fields. Moscow: Nauka 1981
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Arak, T., Surgailis, D. Markov fields with polygonal realizations. Probab. Th. Rel. Fields 80, 543–579 (1989). https://doi.org/10.1007/BF00318906
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DOI: https://doi.org/10.1007/BF00318906
Keywords
- Stochastic Process
- Probability Theory
- Finite Number
- Statistical Theory
- Random Field