Xicheng Zhang

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20212026

most citedCauchy Problem of Stochastic Kinetic Equations

1 citations · 2 across the 6 of their papers we have counts for

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math.PR2026

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…

math.PR2025

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 $R^{2 d} (d \geq 2)$ driven by Brownian motion: $$\mathord{\rm d} X_t=V_t\mat…

math.PR2024

$W_{d}$ -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 $γ$ -order Hölder and dissipative conditions on the coefficients, we derive the $W_{d}$ -conve…

math.PR2024

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…

math.PR2022★ 1 cited

Ergodicity of supercritical SDEs driven by $α$ -stable processes and heavy-tailed sampling

Xiaolong Zhang, Xicheng Zhang

Let $α \in (0, 2)$ and $d \in N$ . Consider the following stochastic differential equation (SDE) driven by $α$ -stable process in $R^{d}$ : $$ dX_t=b(X_t)dt+σ(X_{t-})d L^α_…

math.PR2021★ 1 cited

Cauchy Problem of Stochastic Kinetic Equations