Recursive tree processes and the mean-field limit of stochastic flows

0524245 - ÚTIA 2021 RIV NL eng J - Journal Article
Mach, Tibor - Sturm, A. - Swart, Jan M.
Recursive tree processes and the mean-field limit of stochastic flows.
Electronic Journal of Probability. Roč. 25, č. 1 (2020), č. článku 61. ISSN 1083-6489. E-ISSN 1083-6489
R&D Projects: GA ČR(CZ) GA16-15238S
Institutional support: RVO:67985556
Keywords : mean-field limit * recursive tree process * recursive distributional equation * endogeny * interacting particle systems * cooperative branching
OECD category: Statistics and probability
Impact factor: 1.151, year: 2020
Method of publishing: Open access
http://library.utia.cas.cz/separaty/2020/SI/swart-0524245.pdf https://projecteuclid.org/journals/electronic-journal-of-probability/volume-25/issue-none/Recursive-tree-processes-and-the-mean-field-limit-of-stochastic/10.1214/20-EJP460.full

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.
Permanent Link: http://hdl.handle.net/11104/0308916