Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures

Manh Hong Duong; J. Tugaut

doi:10.1080/17442508.2019.1677663

Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures

Manh Hong Duong, J. Tugaut

Mathematics

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

259 Downloads (Pure)

Abstract

In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.

Original language	English
Journal	Stochastics: an international journal of probablity and stochastic processes
Early online date	22 Oct 2019
DOIs	https://doi.org/10.1080/17442508.2019.1677663
Publication status	E-pub ahead of print - 22 Oct 2019

Keywords

interacting particle systems
McKean-Vlasov dynamics
propagation of chaos
invariant measures

Access to Document

10.1080/17442508.2019.1677663Licence: None: All rights reserved

Duong_&_Tugaut_Coupled_McKean_Vlasov_diffusions_Stochastics:_an_international_journal_of_probablitiy_and_stochastic_processes_2019
This is an Accepted Manuscript of an article published by Taylor & Francis in Stochastics: an international journal of probablity and stochastic processes on 22/10/2019, available online: https://www.tandfonline.com/doi/full/10.1080/17442508.2019.1677663
Accepted author manuscript, 460 KBLicence: None: All rights reserved

https://www.tandfonline.com/doi/full/10.1080/17442508.2019.1677663Licence: None: All rights reserved

Cite this

@article{f230296e0dde477c8d793f91de10f79e,

title = "Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures",

abstract = "In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.",

keywords = "interacting particle systems, McKean-Vlasov dynamics, propagation of chaos, invariant measures",

author = "Duong, {Manh Hong} and J. Tugaut",

year = "2019",

month = oct,

day = "22",

doi = "10.1080/17442508.2019.1677663",

language = "English",

journal = "Stochastics: an international journal of probablity and stochastic processes",

issn = "1744-2508",

publisher = "Taylor & Francis",

}

TY - JOUR

T1 - Coupled McKean-Vlasov diffusions

T2 - wellposedness, propagation of chaos and invariant measures

AU - Duong, Manh Hong

AU - Tugaut, J.

PY - 2019/10/22

Y1 - 2019/10/22

N2 - In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.

AB - In this paper, we study a two-species model in the form of a coupled system of nonlinear stochastic differential equations (SDEs) that arises from a variety of applications such as aggregation of biological cells and pedestrian movements. The evolution of each process is influenced by four different forces, namely an external force, a self-interacting force, a cross-interacting force and a stochastic noise where the two interactions depend on the laws of the two processes. We also consider a many-particle system and a (nonlinear) partial differential equation (PDE) system that associate to the model. We prove the wellposedness of the SDEs, the propagation of chaos of the particle system, and the existence and (non)-uniqueness of invariant measures of the PDE system.

KW - interacting particle systems

KW - McKean-Vlasov dynamics

KW - propagation of chaos

KW - invariant measures

UR - http://www.scopus.com/inward/record.url?scp=85074513746&partnerID=8YFLogxK

U2 - 10.1080/17442508.2019.1677663

DO - 10.1080/17442508.2019.1677663

M3 - Article

SN - 1744-2508

JO - Stochastics: an international journal of probablity and stochastic processes

JF - Stochastics: an international journal of probablity and stochastic processes

ER -

Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures

Abstract

Keywords

Access to Document

Fingerprint

Cite this