A Versatile Stochastic Dissemination Model

• Published in: Methodology and computing in applied probability Vol. 25; no. 3; p. 69
• Main Authors: Chan, K. M. D., Mandjes, M. R. H.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.09.2023; Springer Nature B.V
• Subjects: Business and Management; Differential equations; Economic conditions; Economic models; Economics; Electrical Engineering; Life Sciences; Mathematical models; Mathematics and Statistics; Random variables; Recessions; Statistics; Wealth distribution; Stochastic dissemination model; 60Gxx; 92D25; 68M20; Wealth distribution; Opinion dynamics; Markov modulation; File storage systems
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-023-10041-2

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).