Open Access
2020 Recursive tree processes and the mean-field limit of stochastic flows
Tibor Mach, Anja Sturm, Jan M. Swart
Electron. J. Probab. 25: 1-63 (2020). DOI: 10.1214/20-EJP460


Interacting particle systems can often be constructed from a graphical representation, by applying local maps at the times of associated Poisson processes. This leads to a natural coupling of systems started in different initial states. We consider interacting particle systems on the complete graph in the mean-field limit, i.e., as the number of vertices tends to infinity. We are not only interested in the mean-field limit of a single process, but mainly in how several coupled processes behave in the limit. This turns out to be closely related to recursive tree processes as studied by Aldous and Bandyopadyay in discrete time. We here develop an analogue theory for recursive tree processes in continuous time. We illustrate the abstract theory on an example of a particle system with cooperative branching. This yields an interesting new example of a recursive tree process that is not endogenous.


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Tibor Mach. Anja Sturm. Jan M. Swart. "Recursive tree processes and the mean-field limit of stochastic flows." Electron. J. Probab. 25 1 - 63, 2020.


Received: 30 December 2018; Accepted: 20 April 2020; Published: 2020
First available in Project Euclid: 13 May 2020

zbMATH: 1446.82054
MathSciNet: MR4112765
Digital Object Identifier: 10.1214/20-EJP460

Primary: 82C22
Secondary: 60J25 , 60J80 , 60K35

Keywords: cooperative branching , endogeny , interacting particle systems , Mean-field limit , recursive distributional equation , recursive tree process

Vol.25 • 2020
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