相关论文: Error estimates of the backward Euler-Maruyama met…

In this paper we consider the Euler-Maruyama scheme for a class ofstochastic delay differential equations driven by a fractional Brownian motion with index $H\in(0,1)$. We establish the consistency of the scheme and study the rate of…

We consider one-step methods for integrating stochastic differential equations and prove pathwise convergence using ideas from rough path theory. In contrast to alternative theories of pathwise convergence, no knowledge is required of…

We study the strong approximation of stochastic differential equations with discontinuous drift coefficients and (possibly) degenerate diffusion coefficients. To account for the discontinuity of the drift coefficient we construct an…

The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both the drift and the diffusion coefficient are allowed to grow super-linearly. The existence and…

We study the strong convergence order of the Euler-Maruyama scheme for scalar stochastic differential equations with additive noise and irregular drift. We provide a general framework for the error analysis by reducing it to a weighted…

The strong convergence of the semi-implicit Euler-Maruyama (EM) method for stochastic differential equations with non-linear coefficients driven by a class of L\'evy processes is investigated. The dependence of the convergence order of the…

In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to the mean square norm is determined to be $\frac{1}{2}$ for…

For numerical approximations to stochastic differential equations using the Euler-Maruyama scheme, we propose incorporating approximate random variables computed using low precisions, such as single and half precision. We propose and…

We prove strong convergence of order $1/4-\epsilon$ for arbitrarily small $\epsilon>0$ of the Euler-Maruyama method for multidimensional stochastic differential equations (SDEs) with discontinuous drift and degenerate diffusion coefficient.…

In this paper numerical methods for solving stochastic differential equations with Markovian switching (SDEwMSs) are developed by pathwise approximation. The proposed family of strong predictor-corrector Euler-Maruyama methods is designed…

This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes several equations with super-linearly growing drift and diffusion…

We study the error between the exact solution and its Euler-Maruyama approximation in temporal-spatial H\"older-norms for L\'evy-driven stochastic differential equations.

An implicit Euler--Maruyama method with non-uniform step-size applied to a class of stochastic partial differential equations is studied. A spectral method is used for the spatial discretization and the truncation of the Wiener process. A…

An Euler-type framework with equidistant step sizes is proposed for a class of time-changed stochastic differential equations.We establish the strong convergence rate of the standard Euler--Maruyama method under the global Lipschitz…

In this paper, we extend the logarithmic Euler-Maruyama scheme for stochastic delay differential equation in one dimension to the part where we propose a scheme for a system of stochastic delay differential equations. We then show that the…

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…

We study the strong rates of the Euler-Maruyama approximation for one dimensional stochastic differential equations whose drift coefficient may be neither continuous nor one-sided Lipschitz and diffusion coefficient is H\"older continuous.…

We consider the Euler-Maruyama approximation for multi-dimensional stochastic differential equations with irregular coefficients. We provide the rate of strong convergence where the possibly discontinuous drift coefficient satisfies a…

The exponential stability of numerical methods to stochastic differential equations (SDEs) has been widely studied. In contrast, there are relatively few works on polynomial stability of numerical methods. In this letter, we address the…

In this paper we study the strong convergence for the Euler-Maruyama approximation of a class of stochastic differential equations whose both drift and diffusion coefficients are possibly discontinuous.