Zobrazeno 1 - 10
of 465
pro vyhledávání: '"Hong, Jialin"'
This paper investigates the structure preservation and convergence analysis of a class of fully discrete finite difference schemes for the stochastic heat equation driven by L\'evy space-time white noise. The novelty lies in the simultaneous preserva
Externí odkaz:
http://arxiv.org/abs/2409.14064
The asymptotic error distribution of numerical methods applied to stochastic ordinary differential equations has been well studied, which characterizes the evolution pattern of the error distribution in the small step-size regime. It is still open fo
Externí odkaz:
http://arxiv.org/abs/2409.13827
In this manuscript, we propose efficient stochastic semi-explicit symplectic schemes tailored for nonseparable stochastic Hamiltonian systems (SHSs). These semi-explicit symplectic schemes are constructed by introducing augmented Hamiltonians and usi
Externí odkaz:
http://arxiv.org/abs/2405.14484
The superiority of stochastic symplectic methods over non-symplectic counterparts has been verified by plenty of numerical experiments, especially in capturing the asymptotic behaviour of the underlying solution process. How can one theoretically exp
Externí odkaz:
http://arxiv.org/abs/2404.14842
This paper investigates longtime behaviors of the $\theta$-Euler-Maruyama method for the stochastic functional differential equation with superlinearly growing coefficients. We focus on the longtime convergence analysis in mean-square sense and weak
Externí odkaz:
http://arxiv.org/abs/2404.08891
It is known from the monograph [1, Chapter 5] that the weak convergence analysis of numerical schemes for stochastic Maxwell equations is an unsolved problem. This paper aims to fill the gap by establishing the long-time weak convergence analysis of
Externí odkaz:
http://arxiv.org/abs/2403.09293
For stochastic wave equation, when the dissipative damping is a non-globally Lipschitz function of the velocity, there are few results on the long-time dynamics, in particular, the exponential ergodicity and strong law of large numbers, for the equat
Externí odkaz:
http://arxiv.org/abs/2402.01137
In order to give quantitative estimates for approximating the ergodic limit, we investigate probabilistic limit behaviors of time-averaging estimators of numerical discretizations for a class of time-homogeneous Markov processes, by studying the corr
Externí odkaz:
http://arxiv.org/abs/2310.08227
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 estimate for the exact solution via analyzing the associated convolution st
Externí odkaz:
http://arxiv.org/abs/2308.16696