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math.NA2023
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…
math.NA2023★ 2 cited
Asymptotics of large deviations of finite difference method for stochastic Cahn--Hilliard equation
Diancong Jin, Derui Sheng
In this work, we establish the Freidlin--Wentzell large deviations principle (LDP) of the stochastic Cahn--Hilliard equation with small noise, which implies the one-point LDP. Furt…
math.NA2023
Superiority Of Symplectic Methods For Stochastic Hamiltonian System Via Asymptotic Error Distribution
Jialin Hong, Ge Liang, Derui Sheng
The superiority of symplectic methods for stochastic Hamiltonian systems has been widely recognized, yet the probabilistic mechanism behind this superiority remains incompletely un…