Guohuan Zhao

collaborators

6 papers

math.AP2026

On the Schauder Estimates for Non-local Equations with Drift: The Supercritical Case

Yanfang Li, Guohuan Zhao

We establish a Schauder estimate for a nonlocal Cauchy problem with drift. The leading operator is the generator of a non-degenerate $α$ -stable process with $α \in (0, 1)$ , and the dr…

math.PR2026

Stein's Method for Convergence Rates of Invariant Measures in the Nonlocal-to-Local Limit

Mingyan Wu, Guohuan Zhao

We utilize Stein's method to establish quantitative bounds on the total variation distance between the invariant measure of a drifted nonlocal Markov operator and that of its local…

math.PR2025

SDEs with critical time dependent drifts: strong solutions

Michael RÃ¶ckner, Guohuan Zhao

Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the unique strong solvability of time-inhomogeneous stochastic differential equ…

math.PR2025

Non-local operators with low singularity kernels: regularity estimates and martingale problem

Eryan Hu, Guohuan Zhao

We consider the linear non-local operator $L$ denoted by \[ \mathcal{L} u (x) = \int_{\mathbb{R}^d} \left(u(x+z)-u(x)\right) a(x,z)J(z)\,d z. \] Here $a (x, z)$ is bounded…

math.PR2025

Stochastic Lagrangian Flows for SDEs with rough coefficients

Guohuan Zhao

We prove the existence and uniqueness of Stochastic Lagrangian Flows and almost everywhere Stochastic Flows for non-degenearted SDEs with rough coefficients. As an application of o…

math.PR2025

Dirichlet heat kernel estimates for rectilinear stable processes

Zhen-Qing Chen, Eryan Hu, Guohuan Zhao

Let $d \geq 2$ , $I^\pm \in (0, 2)$ , and $X$ be the rectilinear $I^\pm$ -stable process on $R^{d}$ . We first present a geometric characterization of an open subset $D\subset \mathbb{R…