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Markov Chains and Kinetic Theory: A Possible Application to Socio-Economic Problems

Author

Listed:
  • Bruno Carbonaro

    (Dipartimento di Matematica e Fisica, Università degli Studi della Campania “L. Vanvitelli”, Viale Lincoln 5, 81100 Caserta, Italy
    These authors contributed equally to this work.)

  • Marco Menale

    (Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Via Cintia, Monte S. Angelo, 80126 Naples, Italy
    These authors contributed equally to this work.)

Abstract

A very important class of models widely used nowadays to describe and predict, at least in stochastic terms, the behavior of many-particle systems (where the word “particle” is not meant in the purely mechanical sense: particles can be cells of a living tissue, or cars in a traffic flow, or even members of an animal or human population) is the Kinetic Theory for Active Particles, i.e., a scheme of possible generalizations and re-interpretations of the Boltzmann equation. Now, though in the literature on the subject this point is systematically disregarded, this scheme is based on Markov Chains, which are special stochastic processes with important properties they share with many natural processes. This circumstance is here carefully discussed not only to suggest the different ways in which Markov Chains can intervene in equations describing the stochastic behavior of any many-particle system, but also, as a preliminary methodological step, to point out the way in which the notion of a Markov Chain can be suitably generalized to this aim. As a final result of the discussion, we find how to develop new very plausible and likely ways to take into account possible effects of the external world on a non-isolated many-particle system, with particular attention paid to socio-economic problems.

Suggested Citation

  • Bruno Carbonaro & Marco Menale, 2024. "Markov Chains and Kinetic Theory: A Possible Application to Socio-Economic Problems," Mathematics, MDPI, vol. 12(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1571-:d:1396975
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    References listed on IDEAS

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    1. Nicola Bellomo & Maria Bertotti & Marcello Delitala, 2007. "From the kinetic theory of active particles to the modeling of social behaviors and politics," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(4), pages 545-555, August.
    2. Menale, Marco & Munafò, Carmelo Filippo, 2023. "A kinetic framework under the action of an external force field: Analysis and application in epidemiology," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    3. G. Dimarco & L. Pareschi & G. Toscani & M. Zanella, 2020. "Wealth distribution under the spread of infectious diseases," Papers 2004.13620, arXiv.org.
    4. Sajid, Zaman & Khan, Faisal & Zhang, Yan, 2017. "Integration of interpretive structural modelling with Bayesian network for biodiesel performance analysis," Renewable Energy, Elsevier, vol. 107(C), pages 194-203.
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