18 citations · 32 across the 9 of their papers we have counts for
9 papers
Fundamental weak convergence theorem for stochastic Volterra integral equations and its applications
Xinjie Dai, Qijiao Yin, Diancong Jin
We study weak convergence rates of numerical approximations for stochastic Volterra integral equations (SVIEs), a class of non-Markovian models that arises naturally in stochastic…
Splitting AVF method for generalized Langevin equations: probability density function and geometric ergodicity
Xinjie Dai, Xingyu Liu, Diancong Jin +1
The generalized Langevin equation (GLE) constitutes a fundamental model for describing nonequilibrium dynamics with memory effects. To overcome the numerical challenges arising fro…
Asymptotic error distribution of Mittag--Leffler Euler method for a fractional stochastic differential equation
Xinjie Dai, Baiping Zhang, Diancong Jin
In this paper, we investigate the asymptotic distribution of the normalized error for the Mittag--Leffler Euler (MLE) method applied to a class of multidimensional fractional stoch…
Strong convergence rate of the positivity-preserving logarithmic truncated EM method for multi-dimensional stochastic differential equations with positive solutions
Xingwei Hu, Xinjie Dai, Aiguo Xiao
As a combination of the logarithmic transformation with the truncated Euler-Maruyama (TEM) scheme, the positivity-preserving logarithmic truncated Euler-Maruyama (LTEM) scheme has…
Strong convergence rate of positivity-preserving truncated Euler--Maruyama method for multi-dimensional stochastic differential equations with positive solutions
Xingwei Hu, Xinjie Dai, Aiguo Xiao
To construct positivity-preserving numerical methods, a vast majority of existing works employ transformation techniques such as the Lamperti transformation or logarithmic transfor…
Error analysis of numerical methods on graded meshes for stochastic Volterra equations
Xinjie Dai, Jialin Hong, Derui Sheng
This paper presents the error analysis of numerical methods on graded meshes for stochastic Volterra equations with weakly singular kernels. We first prove a novel regularity estim…
Mittag--Leffler Euler integrator and large deviations for stochastic space-time fractional diffusion equations
Xinjie Dai, Jialin Hong, Derui Sheng
Stochastic space-time fractional diffusion equations often appear in the modeling of the heat propagation in non-homogeneous medium. In this paper, we firstly investigate the Mitta…
Strong error analysis of Euler methods for overdamped generalized Langevin equations with fractional noise: Nonlinear case
Xinjie Dai, Jialin Hong, Derui Sheng +1
This paper considers the strong error analysis of the Euler and fast Euler methods for nonlinear overdamped generalized Langevin equations driven by the fractional noise. The main…
Stochastic fractional integro-differential equations with weakly singular kernels: Well-posedness and Euler--Maruyama approximation
Xinjie Dai, Aiguo Xiao, Weiping Bu
This paper considers the initial value problem of general nonlinear stochastic fractional integro-differential equations with weakly singular kernels. Our effort is devoted to esta…