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A collision-oriented interacting particle system for Landau-type equations and the molecular chaos
Kai Du, Lei Li
We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisi…
Empirical approximation to invariant measures of mean-field Langevin dynamics
Wenjing Cao, Kai Du
This paper is concerned with the approximation to invariant measures for Langevin dynamics of McKean--Vlasov type. Under dissipativity and Lipschitz conditions, we prove that the e…
Sequential propagation of chaos
Kai Du, Yifan Jiang, Xiaochen Li
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting p…
Empirical approximation to invariant measures for McKean--Vlasov processes: mean-field interaction vs self-interaction
Kai Du, Yifan Jiang, Jinfeng Li
This paper proves that, under a monotonicity condition, the invariant probability measure of a McKean--Vlasov process can be approximated by weighted empirical measures of some pro…