3 citations · 6 across the 9 of their papers we have counts for
12 papers
Quantitative Propagation of Chaos and Fluctuations for Kinetic McKean--Vlasov SDEs with Singular Interaction Kernels
Zimo Hao, Xicheng Zhang, Xianliang Zhao
We prove a quantitative propagation of chaos estimate and a central limit theorem for the particle system associated with a class of degenerate kinetic McKean--Vlasov SDEs with ext…
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^{2d…
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: $$\mathord{\rm d} X_t=V_t\mat…
-convergence rate of EM schemes for invariant measures of supercritical stable SDEs
Peng Chen, Lihu Xu, Xiaolong Zhang +1
By establishing the regularity estimates for nonlocal Stein/Poisson equations under -order Hölder and dissipative conditions on the coefficients, we derive the -conve…
Heat kernel estimates for nonlocal kinetic operators
Haojie Hou, Xicheng Zhang
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ Δ^{α/2}_v + v \cdot \nabla_x…
Averaging principle for SDEs with singular drifts driven by -stable processes
Mengyu Cheng, Zimo Hao, Xicheng Zhang
In this paper, we investigate the convergence rate of the averaging principle for stochastic differential equations (SDEs) with -Hölder drift driven by -stable processes. Mor…
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…
Heat kernel estimates for kinetic SDEs with drifts being unbounded and in Kato's class
Chongyang Ren, Xicheng Zhang
In this paper we investigate the existence and uniqueness of weak solutions for kinetic stochastic differential equations with Hölder diffusion and unbounded singular drifts in Kat…
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 $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqr…
Ergodicity of supercritical SDEs driven by -stable processes and heavy-tailed sampling
Xiaolong Zhang, Xicheng Zhang
Let and . Consider the following stochastic differential equation (SDE) driven by -stable process in : $$ dX_t=b(X_t)dt+σ(X_{t-})d L^α_…
Cauchy Problem of Stochastic Kinetic Equations
Xiaolong Zhang, Xicheng Zhang
In this paper we establish the optimal regularity estimates for the Cauchy problem of stochastic kinetic equations with random coefficients in anisotropic Besov spaces. As applicat…
Heat kernel of supercritical SDEs with unbounded drifts
Stéphane Menozzi, Zhang Xicheng
Let and . Consider the following SDE in :where is a $d…