66 citations · 454 across the 28 of their papers we have counts for
29 papers
Linear implicit approximations of invariant measures of semi-linear SDEs with non-globally Lipschitz coefficients
Chenxu Pang, Xiaojie Wang, Yue Wu
This article investigates the weak approximation towards the invariant measure of semi-linear stochastic differential equations (SDEs) under non-globally Lipschitz coefficients. Fo…
An unconditional boundary and dynamics preserving scheme for the stochastic epidemic model
Ruishu Liu, Xiaojie Wang, Lei Dai
In the present article, we construct a logarithm transformation based Milstein-type method for the stochastic susceptible-infected-susceptible (SIS) epidemic model evolving in the…
Strong convergence rates for a full discretization of stochastic wave equation with nonlinear damping
Meng Cai, David Cohen, Xiaojie Wang
The paper establishes the strong convergence rates of a spatio-temporal full discretization of the stochastic wave equation with nonlinear damping in dimension one and two. We disc…
Order-One Convergence of the Backward Euler Method for Random Periodic Solutions of Semilinear SDEs
Yujia Guo, Xiaojie Wang, Yue Wu
In this paper, we revisit the backward Euler method for numerical approximations of random periodic solutions of semilinear SDEs with additive noise. Improved -estimates of…
Antithetic multilevel Monte Carlo method for approximations of SDEs with non-globally Lipschitz continuous coefficients
Chenxu Pang, Xiaojie Wang
In the field of computational finance, one is commonly interested in the expected value of a financial derivative whose payoff depends on the solution of stochastic differential eq…
Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients
Xiaojie Wang, Yuying Zhao, Zhongqiang Zhang
We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Mils…
Weak error estimates of fully-discrete schemes for the stochastic Cahn-Hilliard equation
Charles-Edouard Bréhier, Jianbo Cui, Xiaojie Wang
We study a class of fully-discrete schemes for the numerical approximation of solutions of stochastic Cahn--Hilliard equations with cubic nonlinearity and driven by additive noise.…
Strong convergence rates of a fully discrete scheme for the Cahn-Hilliard-Cook equation
Ruisheng Qi, Meng Cai, Xiaojie Wang
The first aim of this paper is to examine existence, uniqueness and regularity for the Cahn-Hilliard-Cook (CHC) equation in space dimension . By applying a spectral Galerk…
Strong convergence rates of an explicit scheme for stochastic Cahn--Hilliard equation with additive noise
Meng Cai, Ruisheng Qi, Xiaojie Wang
In this paper, we propose and analyze an explicit time-stepping scheme for a spatial discretization of stochastic Cahn--Hilliard equation with additive noise. The fully discrete ap…
Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients
Xiaojie Wang, Yuying Zhao, Zhongqiang Zhang
We present an error analysis of weak convergence of one-step numerical schemes for stochastic differential equations (SDEs) with super-linearly growing coefficients. Following Mils…
Mean-square convergence rates of implicit Milstein type methods for SDEs with non-Lipschitz coefficients
Xiaojie Wang
A class of implicit Milstein type methods is introduced and analyzed in the present article for stochastic differential equations (SDEs) with non-globally Lipschitz drift and diffu…
On the backward Euler method for a generalized Ait-Sahalia-type rate model with Poisson jumps
Yuying Zhao, Xiaojie Wang, Mengchao Wang
This article aims to reveal the mean-square convergence rate of the backward Euler method (BEM) for a generalized Ait-Sahaliz interest rate model with Poisson jumps. The main diffi…
Weak convergence rates for an explicit full-discretization of stochastic Allen-Cahn equation with additive noise
Meng Cai, Siqing Gan, Xiaojie Wang
We discretize the stochastic Allen-Cahn equation with additive noise by means of a spectral Galerkin method in space and a tamed version of the exponential Euler method in time. Th…
Error estimates of semi-discrete and fully discrete finite element methods for the Cahn-Hilliard-Cook equation
Ruisheng Qi, Xiaojie Wang
In two recent publications [Kov{á}cs, Larsson, and Mesforush, SIAM J. Numer. Anal. 49(6), 2407-2429, 2011] and [Furihata, et al., SIAM J. Numer. Anal. 56(2), 708-731, 2018], strong…
Mean-square approximations of Lévy noise driven SDEs with super-linearly growing diffusion and jump coefficients
Ziheng Chen, Siqing Gan, Xiaojie Wang
This paper first establishes a fundamental mean-square convergence theorem for general one-step numerical approximations of Lévy noise driven stochastic differential equations with…
A full-discrete exponential Euler approximation of invariant measure for parabolic stochastic partial differential equations
Ziheng Chen, Siqing Gan, Xiaojie Wang
We discrete the ergodic semilinear stochastic partial differential equations in space dimension with additive noise, spatially by a spectral Galerkin method and temporal…
Optimal error estimates of Galerkin finite element methods for stochastic Allen-Cahn equation with additive noise
Ruisheng Qi, Xiaojie Wang
Strong approximation errors of both finite element semi-discretization and spatio-temporal full discretization are analyzed for the stochastic Allen-Cahn equation driven by additiv…
An efficient explicit full-discrete scheme for strong approximation of stochastic Allen-Cahn equation
Xiaojie Wang
In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced an…
Sharp mean-square regularity results for SPDEs with fractional noise and optimal convergence rates for the numerical approximations
Xiaojie Wang, Ruisheng Qi, Fengze Jiang
This article offers sharp spatial and temporal mean-square regularity results for a class of semi-linear parabolic stochastic partial differential equations (SPDEs) driven by infin…
An accelerated exponential time integrator for semi-linear stochastic strongly damped wave equation with additive noise
Ruisheng Qi, Xiaojie Wang
This paper is concerned with the strong approximation of a semi-linear stochastic wave equation with strong damping, driven by additive noise. Based on a spatial discretization per…
Error estimates of finite element method for semi-linear stochastic strongly damped wave equation
Ruisheng Qi, Xiaojie Wang
In this paper, we consider a semi-linear stochastic strongly damped wave equation driven by additive Gaussian noise. Following a semigroup framework, we establish existence, unique…
Full discretisation of semi-linear stochastic wave equations driven by multiplicative noise
Rikard Anton, David Cohen, Stig Larsson +1
A fully discrete approximation of the semi-linear stochastic wave equation driven by multiplicative noise is presented. A standard linear finite element approximation is used in sp…
An exponential integrator scheme for time discretization of nonlinear stochastic wave equation
Xiaojie Wang
This work is devoted to convergence analysis of an exponential integrator scheme for semi-discretization in time of nonlinear stochastic wave equation. A unified framework is first…
On Uniqueness of Complete Ricci Flow Solution with Curvature Bounded from Below
Li Sheng, Xiaojie Wang
Let be a complete noncompact non-collapsing -dimensional riemannian manifold, whose complex sectional curvature is bounded from below and scalar curvature is bounded fro…