LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT

Rangel Baldasso; Alan Pereira; Guilherme Reis

doi:10.1214/21-AAP1692

LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT

Rangel Baldasso
, Alan Pereira
, Guilherme Reis

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the pathdependent McKean-Vlasov diffusion associated to the system. As corollary, we obtain a strong law of large numbers for the sequence of empirical measures. The proof is based on a decoupling technique by associating to the system a convenient family of product measures. To illustrate, we apply our results for the delayed stochastic Kuramoto model and for a SDE version of Galves-Löcherbach model.

Original language	English
Pages (from-to)	665-695
Number of pages	31
Journal	Annals of Applied Probability
Volume	32
Issue number	1
DOIs	https://doi.org/10.1214/21-AAP1692
State	Published - Feb 2022

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2022.

Funding

Funding. RB is supported by the Israel Science Foundation through grant 575/16 and by the German Israeli Foundation through grant I-1363-304.6/2016. AP was partially supported by Capes/PNPD fellowship 88882.315944/2019-01. GR is supported by a Capes/PNPD fellowship 888887.313738/2019-00. The authors thank IMPA for hospitality and financial support in the early stages of the work.

Funders	Funder number
German Israeli Foundation	888887.313738/2019-00, 88882.315944/2019-01, I-1363-304.6/2016
Israel Science Foundation	575/16

Keywords

McKean-Vlasov diffusions
Path-dependent SDEs

Access to Document

10.1214/21-AAP1692

Cite this

@article{397f6ed19e7045c9bd3414e628828a4f,

title = "LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT",

abstract = "We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the pathdependent McKean-Vlasov diffusion associated to the system. As corollary, we obtain a strong law of large numbers for the sequence of empirical measures. The proof is based on a decoupling technique by associating to the system a convenient family of product measures. To illustrate, we apply our results for the delayed stochastic Kuramoto model and for a SDE version of Galves-L{\"o}cherbach model.",

keywords = "McKean-Vlasov diffusions, Path-dependent SDEs",

author = "Rangel Baldasso and Alan Pereira and Guilherme Reis",

note = "Publisher Copyright: {\textcopyright} Institute of Mathematical Statistics, 2022.",

year = "2022",

month = feb,

doi = "10.1214/21-AAP1692",

language = "אנגלית",

volume = "32",

pages = "665--695",

journal = "Annals of Applied Probability",

issn = "1050-5164",

publisher = "Institute of Mathematical Statistics",

number = "1",

}

TY - JOUR

T1 - LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT

AU - Baldasso, Rangel

AU - Pereira, Alan

AU - Reis, Guilherme

PY - 2022/2

Y1 - 2022/2

N2 - We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the pathdependent McKean-Vlasov diffusion associated to the system. As corollary, we obtain a strong law of large numbers for the sequence of empirical measures. The proof is based on a decoupling technique by associating to the system a convenient family of product measures. To illustrate, we apply our results for the delayed stochastic Kuramoto model and for a SDE version of Galves-Löcherbach model.

AB - We consider a mean-field system of path-dependent stochastic interacting diffusions in random media over a finite time window. The interaction term is given as a function of the empirical measure and is allowed to be nonlinear and path dependent. We prove that the sequence of empirical measures of the full trajectories satisfies a large deviation principle with explicit rate function. The minimizer of the rate function is characterized as the pathdependent McKean-Vlasov diffusion associated to the system. As corollary, we obtain a strong law of large numbers for the sequence of empirical measures. The proof is based on a decoupling technique by associating to the system a convenient family of product measures. To illustrate, we apply our results for the delayed stochastic Kuramoto model and for a SDE version of Galves-Löcherbach model.

KW - McKean-Vlasov diffusions

KW - Path-dependent SDEs

UR - https://www.scopus.com/pages/publications/85126623759

U2 - 10.1214/21-AAP1692

DO - 10.1214/21-AAP1692

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85126623759

SN - 1050-5164

VL - 32

SP - 665

EP - 695

JO - Annals of Applied Probability

JF - Annals of Applied Probability

IS - 1

ER -

LARGE DEVIATIONS FOR INTERACTING DIFFUSIONS WITH PATH-DEPENDENT MCKEAN-VLASOV LIMIT

Abstract

Bibliographical note

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this