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Interpretation of the Evolution of the Homogeneous Markov System (or, equivalently, of the Embedded Markov Chain) as the Deformation of a Viscoelastic Medium. The 3-D Case

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  • K. Loumponias

    (Aristotle University of Thessaloniki)

  • G. Tsaklidis

    (Aristotle University of Thessaloniki)

Abstract

Every attainable structure of a continuous time homogeneous Markov chain (HMC) with n states, or of a closed Markov system with an embedded HMC with n states, or more generally of a Markov system driven by an HMC, is considered as a point-particle of ℜ n . Then, the motion of the attainable structure corresponds to the motion of the respective point-particle in ℜ n . Under the assumption that “the motion of every particle at every time point is due to the interaction with its surroundings”, ℜ n (and equivalently the set of the accosiated attainable structures of the homogeneous Markov system (HMS), or alternatively of the underlying embedded HMC) becomes a continuum. Thus, the evolution of the set of the attainable structures corresponds to the motion of the continuum. In this paper it is shown that the evolution of a three-dimensional HMS (n = 3) or simply of an HMC, can be interpreted through the evolution of a two-dimensional isotropic viscoelastic medium.

Suggested Citation

  • K. Loumponias & G. Tsaklidis, 2017. "Interpretation of the Evolution of the Homogeneous Markov System (or, equivalently, of the Embedded Markov Chain) as the Deformation of a Viscoelastic Medium. The 3-D Case," Methodology and Computing in Applied Probability, Springer, vol. 19(4), pages 1227-1239, December.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:4:d:10.1007_s11009-017-9568-1
    DOI: 10.1007/s11009-017-9568-1
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