5 papers
Quantitative Propagation of Chaos and Fluctuations for Kinetic McKean--Vlasov SDEs with Singular Interaction Kernels
Zimo Hao, Xicheng Zhang, Xianliang Zhao
The paper establishes quantitative bounds on how particle systems approximate kinetic McKean–Vlasov stochastic differential equations with singular interaction kernels, and proves…
Kinetic Fokker-Planck Equations with Nonlinear Diffusion
Zimo Hao, Zhengyan Wu, Xicheng Zhang
We study existence, regularity, and uniqueness for the nonlinear kinetic Fokker--Planck equation on $\mathbb R^{…
Propagation of chaos for moderately interacting particle systems related to singular kinetic McKean-Vlasov SDEs
Zimo Hao, Jean-Francois Jabir, Stéphane Menozzi +2
This work addresses the propagation of chaos properties in a class of moderately interacting particle systems for the approximation of singular kinetic McKean-Vlasov SDEs driven by…
Kinetic SDEs with subcritical distributional drifts
Zikai Chen, Zimo Hao, Xicheng Zhang
In this paper we study the well-posedness of the kinetic stochastic differential equation (SDE) in driven by Brownian motion: $$\mathord{\rm d} X_t=V_t\mat…
SDEs with supercritical distributional drifts
Zimo Hao, Xicheng Zhang
Let . In this paper, we investigate the following stochastic differential equation (SDE) in driven by Brownian motion $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqr…