Large deviations for singularly interacting diffusions

Jasper Hoeksema; Thomas Holding; Mario Maurelli; Oliver Tse

doi:10.1214/22-AIHP1319

Large deviations for singularly interacting diffusions

Jasper Hoeksema, Thomas Holding, Mario Maurelli, Oliver Tse

Onderzoeksoutput: Bijdrage aan tijdschrift › Tijdschriftartikel › Academic › peer review

37 Downloads (Pure)

Samenvatting

In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean–Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently a LDP for Gibbs and Gibbs-like measures with singular potentials.

Originele taal-2	Engels
Pagina's (van-tot)	492-548
Aantal pagina's	57
Tijdschrift	Annales de l'institut Henri Poincare (B): Probability and Statistics
Volume	60
Nummer van het tijdschrift	1
DOI's	https://doi.org/10.1214/22-AIHP1319
Status	Gepubliceerd - feb. 2024

Toegang tot document

10.1214/22-AIHP1319

pdfDefinitieve gepubliceerde versie, 710 KB

Andere bestanden en links

Link naar publicatie in Scopus

Citeer dit

@article{d0e22c6fcf154b099468a9545307374d,

title = "Large deviations for singularly interacting diffusions",

abstract = "In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean–Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently a LDP for Gibbs and Gibbs-like measures with singular potentials.",

keywords = "Gibbs measures, Large deviations, McKean–Vlasov interacting diffusions, Singular drift, Varadhan lemma",

author = "Jasper Hoeksema and Thomas Holding and Mario Maurelli and Oliver Tse",

year = "2024",

month = feb,

doi = "10.1214/22-AIHP1319",

language = "English",

volume = "60",

pages = "492--548",

journal = "Annales de l'institut Henri Poincare (B): Probability and Statistics",

issn = "0246-0203",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - Large deviations for singularly interacting diffusions

AU - Hoeksema, Jasper

AU - Holding, Thomas

AU - Maurelli, Mario

AU - Tse, Oliver

PY - 2024/2

Y1 - 2024/2

N2 - In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean–Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently a LDP for Gibbs and Gibbs-like measures with singular potentials.

AB - In this paper we prove a large deviation principle (LDP) for the empirical measure of a general system of mean-field interacting diffusions with singular drift (as the number of particles tends to infinity) and show convergence to the associated McKean–Vlasov equation. Along the way, we prove an extended version of the Varadhan Integral Lemma for a discontinuous change of measure and subsequently a LDP for Gibbs and Gibbs-like measures with singular potentials.

KW - Gibbs measures

KW - Large deviations

KW - McKean–Vlasov interacting diffusions

KW - Singular drift

KW - Varadhan lemma

UR - http://www.scopus.com/inward/record.url?scp=85186858636&partnerID=8YFLogxK

U2 - 10.1214/22-AIHP1319

DO - 10.1214/22-AIHP1319

M3 - Article

AN - SCOPUS:85186858636

SN - 0246-0203

VL - 60

SP - 492

EP - 548

JO - Annales de l'institut Henri Poincare (B): Probability and Statistics

JF - Annales de l'institut Henri Poincare (B): Probability and Statistics

IS - 1

ER -

Large deviations for singularly interacting diffusions

Samenvatting

Toegang tot document

Andere bestanden en links

Vingerafdruk

Citeer dit