Zimo Hao

activity

20192026

most citedStrong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

6 citations · 26 across the 25 of their papers we have counts for

collaborators

28 papers

math.AP2026

Harnack estimates for nondivergence kinetic equations

Zimo Hao, Xicheng Zhang

We establish a weak Harnack inequality for nonnegative strong supersolutions and a Harnack inequality for nonnegative strong solutions of the nondivergence-form kinetic equation \[…

math.PR2026

Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts

Zikai Chen, Zimo Hao, Xicheng Zhang

We study the stochastic differential equation $d X_{t} = b (t, X_{t}) d t + 2 d W_{t}$ on $R^{d}$ , where $b$ is a time-dependent, divergence-free distributional drift of critical…

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.AP2026

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 $\partial_{t} f = Δ_{v} Ψ (f) - v \cdot \nabla_{x} f, f ∣_{t = 0} = f_{0},$ on $\mathbb R^{2d…

math.PR2026

Euler--Maruyama scheme for $α$ -stable SDE with distributional drift

Zimo Hao, Mingyan Wu

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $α$ -stable processes (including cylindrical ones) with $α \in (1, 2)$ . We f…

math.PR2026

Weak approximation of kinetic SDEs: closing the criticality gap

Zimo Hao, Khoa Lê, Chengcheng Ling

We study the weak convergence of a generic tamed Euler-Maruyama scheme for kinetic stochastic differential equations (SDEs) with integrable drifts. We show that the marginal densit…

math.PR2025

Kinetic Theory with Fluctuations: Well-Posedness of The Vlasov--Fokker--Planck--Dean--Kawasaki Equations

Zimo Hao, Zhengyan Wu, Johannes Zimmer

We study Vlasov--Fokker--Planck--Dean--Kawasaki equations driven by correlated conservative noise. For regular noise coefficients and bounded nonlocal interactions, we establish pr…

math.PR2025

Strong and weak well-posedness of McKean-Vlasov SDEs driven by $α$ -stable processes under unified condition

Zimo Hao

In this paper, we consider $α \in (0, 2)$ and establish the strong well-posedness of McKean--Vlasov SDEs driven by an $α$ -stable process with a Hölder (Besov) kernel $K \in \mathbf{C…

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.PR2025

Quantitative approximation to density dependent SDEs driven by $α$ -stable processes

Ke Song, Zimo Hao, Mingkun Ye

Based on a class of moderately interacting particle systems, we establish a quantitative approximation for density-dependent McKean-Vlasov SDEs and the corresponding nonlinear, non…

math.PR2024

Supercritical McKean-Vlasov SDE driven by cylindrical $α$ -stable process

Zimo Hao, Chongyang Ren, Mingyan Wu

In this paper, we study the following supercritical McKean-Vlasov SDE, driven by a symmetric non-degenerate cylindrical $α$ -stable process in $R^{d}$ with $α \in (0, 1)$ : $$ \…

math.DS2024

Averaging principle for SDEs with singular drifts driven by $α$ -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 $β$ -Hölder drift driven by $α$ -stable processes. Mor…

math.PR2024

Quantitative approximation of stochastic kinetic equations: from discrete to continuum

Zimo Hao, Khoa Lê, Chengcheng Ling

We study the convergence of a generic tamed Euler-Maruyama (EM) scheme for the kinetic type stochastic differential equations (SDEs) (also known as second order SDEs) with singular…

math.PR2024

Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $α$ -stable additive noise

Ke Song, Zimo Hao

In this paper, we establish the weak convergence rate of density-dependent stochastic differential equations with bounded drift driven by $α$ -stable processes with $α \in (1, 2)$ . The…

math.PR2024

Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations

Zimo Hao, Michael Röckner, Xicheng Zhang

Motivated by the probabilistic representation for solutions of the Navier-Stokes equations, we introduce a novel class of stochastic differential equations that depend on the entir…

math.AP2024

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…

math.PR2023★ 1 cited

SDEs with supercritical distributional drifts

Zimo Hao, Xicheng Zhang

Let $d \geq 2$ . In this paper, we investigate the following stochastic differential equation (SDE) in $R^{d}$ driven by Brownian motion $$ {\rm d} X_t=b(t,X_t){\rm d} t+\sqr…

math.PR2023★ 1 cited

SDE driven by cylindrical $α$ -stable process with distributional drift

Zimo Hao, Mingyan Wu

For $α \in (1, 2)$ , we study the following stochastic differential equation driven by a non-degenerate symmetric $α$ -stable process in $R^{d}$ : \begin{align*} {\rm d} X_t=b(t,…

math.AP2023★ 1 cited

Second order fractional mean-field SDEs with singular kernels and measure initial data

Zimo Hao, Michael Röckner, Xicheng Zhang

In this paper we establish the local and global well-posedness of weak and strong solutions to second order fractional mean-field SDEs with singular/distribution interaction kernel…

math.PR2022★ 5 cited

Strong and weak convergence for averaging principle of DDSDE with singular drift

Mengyu Cheng, Zimo Hao, Michael Röckner

In this paper, we study the averaging principle for distribution dependent stochastic differential equations with drift in localized $L^{p}$ spaces. Using Zvonkin's transformation an…

math.PR2022★ 6 cited

Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Zimo Hao, Michael Röckner, Xicheng Zhang

In this work we show the strong convergence of propagation of chaos for the particle approximation of McKean-Vlasov SDEs with singular $L^{p}$ -interactions as well as for the moderat…

math.PR2021

Well-posedness of density dependent SDE driven by $α$ -stable process with Hölder drifts

Mingyan Wu, Zimo Hao

In this paper, we show the weak and strong well-posedness of density dependent stochastic differential equations driven by $α$ -stable processes with $α \in (1, 2)$ . The existence part…

math.PR2021

Singular kinetic equations and applications

Zimo Hao, Xicheng Zhang, Rongchan Zhu +1

In this paper we study singular kinetic equations on $R^{2 d}$ by the paracontrolled distribution method introduced in \cite{GIP15}. We first develop paracontrolled calculu…

math.PR2020★ 1 cited

Euler scheme for density dependent stochastic differential equations

Zimo Hao, Michael Röckner, Xicheng Zhang

In this paper we show the existence and uniqueness for a class of density dependent SDEs with bounded measurable drift, where the existence part is based on Euler's approximation f…

Harnack estimates for nondivergence kinetic equations

Well-Posedness for SDEs with Logarithmical Critical Distributional Drifts

Quantitative Propagation of Chaos and Fluctuations for Kinetic McKean--Vlasov SDEs with Singular Interaction Kernels

Kinetic Fokker-Planck Equations with Nonlinear Diffusion

Euler--Maruyama scheme for α-stable SDE with distributional drift

Weak approximation of kinetic SDEs: closing the criticality gap

Kinetic Theory with Fluctuations: Well-Posedness of The Vlasov--Fokker--Planck--Dean--Kawasaki Equations

Strong and weak well-posedness of McKean-Vlasov SDEs driven by α-stable processes under unified condition

Kinetic SDEs with subcritical distributional drifts

Quantitative approximation to density dependent SDEs driven by α-stable processes

Supercritical McKean-Vlasov SDE driven by cylindrical α-stable process

Averaging principle for SDEs with singular drifts driven by α-stable processes

Quantitative approximation of stochastic kinetic equations: from discrete to continuum

Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by α-stable additive noise

Distribution-flow dependent SDEs driven by (fractional) Brownian motion and Navier-Stokes equations

Propagation of chaos for moderately interacting particle systems related to singular kinetic McKean-Vlasov SDEs

SDEs with supercritical distributional drifts

SDE driven by cylindrical α-stable process with distributional drift

Second order fractional mean-field SDEs with singular kernels and measure initial data

Strong and weak convergence for averaging principle of DDSDE with singular drift

Strong convergence of propagation of chaos for McKean-Vlasov SDEs with singular interactions

Well-posedness of density dependent SDE driven by α-stable process with Hölder drifts

Singular kinetic equations and applications

Euler scheme for density dependent stochastic differential equations

Euler--Maruyama scheme for $α$ -stable SDE with distributional drift

Strong and weak well-posedness of McKean-Vlasov SDEs driven by $α$ -stable processes under unified condition

Quantitative approximation to density dependent SDEs driven by $α$ -stable processes

Supercritical McKean-Vlasov SDE driven by cylindrical $α$ -stable process

Averaging principle for SDEs with singular drifts driven by $α$ -stable processes

Convergence rate of the Euler-Maruyama scheme to density dependent SDEs driven by $α$ -stable additive noise

SDE driven by cylindrical $α$ -stable process with distributional drift

Well-posedness of density dependent SDE driven by $α$ -stable process with Hölder drifts