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A Versatile Stochastic Dissemination Model

Author

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  • K. M. D. Chan

    (Korteweg-de Vries Institute, University of Amsterdam
    Transtrend BV)

  • M. R. H. Mandjes

    (Korteweg-de Vries Institute, University of Amsterdam)

Abstract

This paper considers a highly general dissemination model that keeps track of the stochastic evolution of the distribution of wealth over a set of agents. There are two types of events: (i) units of wealth externally arrive, and (ii) units of wealth are redistributed among the agents, while throughout Markov modulation is allowed. We derive a system of coupled differential equations describing the joint transient distribution of the agents’ wealth values, which translate into linear differential equations when considering the corresponding means and (co-)variances. While our model uses the (economic) terminology of wealth being distributed over agents, we illustrate through a series of examples that it can be used considerably more broadly. Indeed, it also facilitates the analysis of the spread of opinions over a population (thus generalizing existing opinion dynamics models), and the analysis of the dynamics of a file storage system (thus allowing the assessment of the efficacy of storage policies).

Suggested Citation

  • K. M. D. Chan & M. R. H. Mandjes, 2023. "A Versatile Stochastic Dissemination Model," Methodology and Computing in Applied Probability, Springer, vol. 25(3), pages 1-25, September.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:3:d:10.1007_s11009-023-10041-2
    DOI: 10.1007/s11009-023-10041-2
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    References listed on IDEAS

    as
    1. Ghislain Léveillé & José Garrido, 2001. "Recursive Moments of Compound Renewal Sums with Discounted Claims," Scandinavian Actuarial Journal, Taylor & Francis Journals, vol. 2001(2), pages 98-110.
    2. Leveille, Ghislain & Garrido, Jose, 2001. "Moments of compound renewal sums with discounted claims," Insurance: Mathematics and Economics, Elsevier, vol. 28(2), pages 217-231, April.
    3. O. J. Boxma & E. J. Cahen & D. Koops & M. Mandjes, 2019. "Linear Stochastic Fluid Networks: Rare-Event Simulation and Markov Modulation," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 125-153, March.
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