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Coupled McKean-Vlasov diffusions: wellposedness, propagation of chaos and invariant measures. (arXiv:1810.01145v1 [math.AP])
来源于:arXiv
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. 查看全文>>