39 citations · 143 across the 21 of their papers we have counts for
22 papers
Diffusions with Critical Divergence-Free Drifts: Varadhan Asymptotics and Path-Law Singularity
Jintao Feng, Guohuan Zhao
We study the Euclidean Varadhan formula (EVF) and path laws for diffusions with critical divergence-free drifts in dimension . For drifts given by smooth bounded skew-symme…
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 -stable process with , and the dr…
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…
Euler-Maruyama scheme for SDE driven by Lévy process with Hölder drift
Yanfang Li, Guohuan Zhao
This study focuses on approximating solutions to SDEs driven by Lévy processes with Hölder continuous drifts using the Euler-Maruyama scheme. We derive the -error for a broad…
Non-local operators with low singularity kernels: regularity estimates and martingale problem
Eryan Hu, Guohuan Zhao
We consider the linear non-local operator 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 is bounded…
Dirichlet heat kernel estimates for rectilinear stable processes
Zhen-Qing Chen, Eryan Hu, Guohuan Zhao
Let , , and be the rectilinear -stable process on . We first present a geometric characterization of an open subset $D\subset \mathbb{R}^…
SDEs with critical time dependent drifts: strong solutions
Michael Röckner, 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…
SDEs with critical time dependent drifts: weak solutions
Michael Röckner, Guohuan Zhao
We prove the unique weak solvability of time-inhomogeneous stochastic differential equations with additive noises and drifts in critical Lebsgue space $L^q([0,T]; L^{p}(\mathbb{R}^…
Existence and Uniqueness for McKean-Vlasov equations with singular interactions
Guohuan Zhao
We investigate the well-posedness of following McKean-Vlasov equation in : \[ \mathrm{d} X_t=σ(t,X_t, μ_{X_t})\mathrm{d} W_t+b(t, X_t, μ_{X_t}) \mathrm{d} t, \] where…
SDEs with random and irregular coefficients
Guohuan Zhao
We consider Itô uniformly nondegenerate equations with random coefficients. When the coefficients satisfy some low regularity assumptions with respect to the spatial variables and…
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…
-theory of stochastic differential equations
Pengcheng Xia, Longjie Xie, Xicheng Zhang +1
In this paper we show the weak differentiability of the unique strong solution with respect to the starting point as well as Bismut-Elworthy-Li's derivative formula for the fol…
Nonlocal elliptic equation in Hölder space and the martingale problem
Chengcheng Ling, Guohuan Zhao
The well-posedness of nonlocal elliptic equation with singular drift is investigated in Besov-Hölder spaces. As an application, we show the existence and uniqueness for correspondi…
Stochastic Lagrangian path for Leray solutions of 3D Navier-Stokes equations
Xicheng Zhang, Guohuan Zhao
In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution ${\mat…
Regularity properties of jump diffusions with irregular coefficients
Guohuan Zhao
In this paper we investigate the regularity properties of strong solutions to SDEs driven by Lévy processes with irregular drift coefficients. Under some mild conditions, we show t…
Dirichlet problem for supercritical nonlocal operators
Xicheng Zhang, Guohuan Zhao
Let be a bounded -domain. Consider the following Dirichlet initial-boundary problem of nonlocal operators with a drift: $$ \partial_t u={\mathscr L}^{(α)}_κu+b\cdot \nabla…
Weak uniqueness for SDEs driven by supercritical stable processes with Holder drifts
Guohuan Zhao
In this paper, we investigate stochastic differential equations(SDEs) driven by a class of supercritical -stable process(including the rotational symmetric stable process) w…
Moderate maximal inequalities for the Ornstein-Uhlenbeck process
Chen Jia, Guohuan Zhao
The maximal inequalities for diffusion processes have drawn increasing attention in recent years. However, the existing proof of the maximum inequalities for the Ornstein-Uhl…
Heat kernel and ergodicity of SDEs with distributional drifts
Xicheng Zhang, Guohuan Zhao
In this paper we consider the following SDE with distributional drift : where is a bounded conti…
Well-posedness of supercritical SDE driven by Lévy processes with irregular drifts
Zhen-Qing Chen, Xicheng Zhang, Guohuan Zhao
In this paper, we study the following time-dependent stochastic differential equation (SDE) in : $$ d X_{t}= σ_t(X_{t-}) d Z_t + b_t(X_{t})d t, \quad X_{0}=x\in {\bf R}^…
Compact support property of SuperBrownian Motion in random environments
Guohuan Zhao
In this paper, we prove the compact support property for a class of nonlinear SPDE including the equation that the density of one-dimensional Super-Brownian Motion in random enviro…
Conditional limit theorems for critical continuous-state branching processes
Yan-Xia Ren, Ting Yang, Guo-Huan Zhao
In this paper we study the conditional limit theorems for critical continuous-state branching processes with branching mechanism where and is…