 Continuum and thermodynamic limits for a simple random-exchange modelBertram Düring, Nicos Georgiou, Sara Merino-Aceituno and Enrico Scalas Stochastic Processes and their Applications, 2022, vol. 149, issue C, 248-277 Abstract: We discuss various limits of a simple random exchange model that can be used for the distribution of wealth. We start from a discrete state space — discrete time version of this model and, under suitable scaling, we show its functional convergence to a continuous space — discrete time model. Then, we show a thermodynamic limit of the empirical distribution to the solution of a kinetic equation of Boltzmann type. We solve this equation and we show that the solutions coincide with the appropriate limits of the invariant measure for the Markov chain. In this way we complete Boltzmann’s program of deriving kinetic equations from random dynamics for this simple model. Three families of invariant measures for the mean field limit are discovered and we show that only two of those families can be obtained as limits of the discrete system while the third is extraneous. Keywords: Wealth distribution; Mean-field limits; Functional limits; Markov chains; Kinetic equations; Partitions of integers (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:149:y:2022:i:c:p:248-277 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2022.03.015 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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