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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

<a href="/cs/project/GA16-15238S" target="_blank" >GA16-15238S: Kolektivní chování velkých stochastických systémů</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Probability

ISSN

1083-6489

e-ISSN

—

Svazek periodika

25

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

63

Strana od-do

61

Kód UT WoS článku

000532409600001

EID výsledku v databázi Scopus

2-s2.0-85085067190