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

K. Loumponias () and G. Tsaklidis ()
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K. Loumponias: Aristotle University of Thessaloniki
G. Tsaklidis: Aristotle University of Thessaloniki

Methodology and Computing in Applied Probability, 2017, vol. 19, issue 4, 1227-1239

Abstract: 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.

Keywords: Homogeneous Markov system; Viscoelastic medium; Equation of motion; 60K35; 60G99; 82C21; 74A05 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s11009-017-9568-1

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