研究领域

随机分析与随机计算

基金项目

2022-2024 PI，国家自然科学基金优秀青年科学基金项目（海外），“随机偏微分方程的数值分析” [NSFC21AAA00602] 在研

2022-2024 PI，国家自然科学基金青年科学基金项目，“随机Allen-Cahn方程的数值遍历性” [NSFC12101296] 在研

2020-2023 PI，香港研究资助局研究基金，“Long-time Behaviors and Numerical Approximations of Stochastic Phase Field Models” [GRF16308720] 离职终止

2019-2022 PI，香港研究资助局研究基金，“Mathematical and Numerical Analysis of Stochastic Phase Field Models” [GRF16307319] 离职转移 

2019-2022 PI，香港大学研究资助局研究基础设施拨款香港科技大学校内研究资助, “Mathematical and Numerical Analysis of Stochastic Phase Field Models” [IRS20SC39] 离职转移 

南方科技大学课程

2020年秋季学期，MA215，概率论

香港科技大学课程

2020年春季学期，MATH1014，微积分II

2019年秋季学期，MATH1003，微积分与线性代数

2018年秋季学期，MATH1003，微积分与线性代数

发表文章

Z. Liu, Lp-convergence rate of backward Euler schemes for monotone SDEs, BIT (2022), https://doi.org/10.1007/s10543-022-00923-1.

D. Sheng, J. Hong, and Z. Liu, Optimal Hölder continuity and hitting probabilities for SPDEs with rough fractional noises, J. Math. Anal. Appl. 512 (2022), no. 1, Paper No. 126125, 21 pp.

Z. Liu and Z. Qiao, Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise. Stoch. Partial Differ. Equ. Anal. Comput. 9 (2021), no. 3, 559–602.

Y. Cao, J. Hong, and Z. Liu, Well-posedness and finite element approximations for elliptic SPDEs with Gaussian noises, Commun. Math. Res. 36 (2020), no. 2, 113--127.

Z. Liu and Z. Qiao, Strong approximation of monotone stochastic partial differential equations driven by white noise, IMA J. Numer. Anal. 40 (2020), no. 2, 1074--1093.

J. Hong, C. Huang, and Z. Liu, Optimal regularity of stochastic evolution equations in M-type 2 Banach spaces, J. Differential Equations 267 (2019), no. 3, 1955--1971.

J. Cui, J. Hong, Z. Liu, and W. Zhou, Strong convergence rate of splitting schemes for stochastic nonlinear Schr"odinger equations, J. Differential Equations 266 (2019), no. 9, 5625--5663.

J. Hong and Z. Liu, Well-posedness and optimal regularity of stochastic evolution equations with multiplicative noises, J. Differential Equations 266 (2019), no. 8, 4712--4745.

Z. Liu and Z. Qiao, Wong--Zakai approximations of stochastic Allen--Cahn equation, Int. J. Numer. Anal. Model. 16 (2019), no. 5, 681--694.

Y. Cao, J. Hong, and Z. Liu, Finite element approximations for second order stochastic differential equation driven by fractional Brownian motion, IMA J. Numer. Anal. 38 (2018), no. 1, 184--197.

J. Hong, L. Ji, and Z. Liu, Optimal error estimates of conservative local discontinuous Galerkin method for nonlinear Schr"odinger equation, Appl. Numer. Math. 127 (2018), no. 5, 164--178.

X. Niu, J. Cui, J. Hong, and Z. Liu, Explicit pseudo-symplectic methods for stochastic Hamiltonian systems, BIT 58 (2018), no. 1, 163--178.

J. Cui, J. Hong, and Z. Liu, Strong convergence rate of finite difference approximations for stochastic cubic Schr"odinger equations, J. Differential Equations 263 (2017), no. 7, 3687--3713.

Y. Cao, J. Hong, and Z. Liu, Approximating stochastic evolution equations with additive white and rough noises, SIAM J. Numer. Anal. 55 (2017), no. 4, 1958--1981.

J. Cui, J. Hong, Z. Liu, and W. Zhou, Stochastic symplectic and multi-symplectic methods for nonlinear Schr"odinger equation with white noise dispersion, J. Comput. Phys. 342 (2017), no. 8, 267--285.

J. Cui, Z. Liu, L. Miao, and X. Wang, H"older continuity for parabolic Anderson equation with non-Gaussian noise, J. Math. Anal. Appl. 441 (2016), no. 2, 684--691.