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 -