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

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F20%3A00524245" target="_blank" >RIV/67985556:_____/20:00524245 - isvavai.cz</a>
Result on the web
<a href="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" target="_blank" >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</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1214/20-EJP460" target="_blank" >10.1214/20-EJP460</a>

Result language
angličtina
Original language name
Recursive tree processes and the mean-field limit of stochastic flows
Original language description
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.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10103 - Statistics and probability

Project
<a href="/en/project/GA16-15238S" target="_blank" >GA16-15238S: Collective behavior of large stochastic systems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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