8 citations · 9 across the 8 of their papers we have counts for
11 papers
Well-posedness, Regularity, and Strong Approximations of Superlinear Stochastic Reaction-Diffusion Equation
Zhihui Liu
This paper develops a general framework for the well-posedness, regularity, and strong approximation of the stochastic reaction--diffusion equation (SRDE) with superlinear drift an…
Uniform-in-Time Weak and Ergodic Error Estimates of a Nonlinearity-Explicit Full Discretization for Superlinear SPDEs Driven by Multiplicative Noise
Jingjing Cai, Zhihui Liu, Xiaoming Wu
For a class of superlinear SPDEs driven by multiplicative noise, we prove an (essentially) sharp uniform-in-time (UIT) weak convergence rate for the nonlinearity-explicit Galerkin…
Uniform-in-time Strong Error Estimates of Tamed-FEM to Superlinear SPDEs driven by Multiplicative Noise
Jingjing Cai, Zhihui Liu
We establish sharp, uniform-in-time strong error estimates for a nonlinearity-explicit tamed finite element method (FEM) applied to a class of superlinear stochastic partial differ…
Inversions of stochastic processes from ergodic measures of Nonlinear SDEs
Hongyu Liu, Zhihui Liu
We introduce and analyze a novel class of inverse problems for stochastic dynamics: Given the ergodic invariant measure of a stochastic process governed by a nonlinear stochastic o…
Ergodic Estimates of One-Step Numerical Approximations for Superlinear SODEs
Xin Liu, Zhihui Liu
This paper establishes the first-order convergence rate for the ergodic error of numerical approximations to a class of stochastic ODEs (SODEs) with superlinear coefficients and mu…
Non-asymptotic Error Analysis of Explicit Modified Euler Methods for Superlinear and Non-contractive SODEs
Zhihui Liu, Xiaojie Wang, Xiaoming Wu +1
A family of explicit modified Euler methods (MEMs) is constructed for long-time approximations of super-linear SODEs driven by multiplicative noise. The proposed schemes can preser…
Weak Error Estimates of Ergodic Approximations for Monotone Jump-diffusion SODEs
Zhihui Liu, Xiaoming Wu
We first derive the exponential ergodicity of the stochastic theta method (STM) with for monotone jump-diffusion stochastic ordinary differential equations (SODEs) u…
Numerical Ergodicity and Optimal Strong Error Estimates for a Class of Novel Tamed Schemes to Superlinear SPDEs
Zhihui Liu, Jie Shen
We construct a class of novel tamed schemes for superlinear stochastic partial differential equations (SPDEs), including the stochastic Allen--Cahn equation driven by either multip…
Geometric Ergodicity and Strong Error Estimates for Tamed Schemes of Super-linear SODEs
Zhihui Liu, Xiaoming Wu
We construct a family of explicit tamed Euler--Maruyama (TEM) schemes, which can preserve the same Lyapunov structure for super-linear stochastic ordinary differential equations (S…
Numerical Unique Ergodicity of Monotone SDEs driven by Nondegenerate Multiplicative Noise
Zhihui Liu, Zhizhou Liu
We first establish the unique ergodicity of the stochastic theta method (STM) with for monotone SODEs, without growth restriction on the coefficients, driven by non…
Harnack Inequalities and Ergodicity of Stochastic Reaction-Diffusion Equation in
Zhihui Liu
We derive Harnack inequalities for a stochastic reaction-diffusion equation with dissipative drift driven by additive irregular noise in the -space for any . These in…