A Versatile Stochastic Dissemination Model

K. M. D. Chan () and M. R. H. Mandjes
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K. M. D. Chan: Korteweg-de Vries Institute, University of Amsterdam
M. R. H. Mandjes: Korteweg-de Vries Institute, University of Amsterdam

Methodology and Computing in Applied Probability, 2023, vol. 25, issue 3, 1-25

Abstract: 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).

Keywords: Stochastic dissemination model; Wealth distribution; Markov modulation; Opinion dynamics; File storage systems; 60Gxx; 92D25; 68M20 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11009-023-10041-2

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