Stochastic analysis and stochastic computation

Courses in Southern University of Science and Technology

2020 Fall, MA215, Probability Theory

Courses in Hong Kong University of Science and Technology

2020 Spring, MATH1014, Calculus II

2019 Fall, MATH1003, Calculus and Linear Algebra

2018 Fall, MATH1003, Calculus and Linear Algebra

Z. Liu, Harnack inequalities, ergodicity, and contractivity of stochastic reaction-diffusion equation in $L^p$, arXiv:2008.01335.

Z. Liu, Asymptotic log-Harnack inequality for monotone SPDE with multiplicative noise, arXiv:2007.13080.

J. Hong, C. Huang, and Z. Liu, Strong convergence rate for fully discrete scheme of semilinear stochastic evolution equation with multiplicative noise, arXiv:1805.07537.

Z. Liu and Z. Qiao, Strong approximation of monotone stochastic partial differential equations driven by multiplicative noise. Stoch PDE: Anal Comp (2020), https://doi.org/10.1007/s40072-020-00179-2.

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.

Z. Liu and H. Liu, The dimension of the centralizer of a square matrix over a field, Journal of Hubei University (Natural Science) 35 (2013), no. 2, 133--137 (An undergraduate paper).