A versatile stochastic dissemination model

TL;DR

This paper introduces a comprehensive stochastic model for wealth distribution that can be adapted to various domains like opinion spread and file storage, providing a unified analytical framework.

Contribution

It develops a general stochastic dissemination model with coupled differential equations, extending to diverse applications beyond economics.

Findings

Derivation of coupled differential equations for wealth distribution dynamics.

Model's applicability to opinion dynamics and storage systems.

Analytical tools for transient and mean-variance analysis.

Abstract

This paper consider 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).