The Strong Convergence and Stability of Explicit Approximations for Nonlinear Stochastic Delay Differential Equations

Strong convergence rate of the truncated Euler-Maruyama method for stochastic differential delay equations with Poisson jumps

In this paper, we study a class of super-linear stochastic differential delay equations with Poisson jumps (SDDEwPJs). The convergence and rate of the convergence of the truncated Euler-Maruyama numerical solutions to SDDEwPJs are investigated under the generalized Khasminskii-type condition.

具有无限延迟的混合随机函数微分方程：近似与数值计算

Hybrid Stochastic Functional Differential Equations with Infinite Delay: Approximations and Numerics

本文提出了一种通过有限延迟混合SFDE的数值解来近似无限延迟混合SFDE解的新方法，适用于高度非线性情形。

The truncated $θ$-Milstein method for nonautonomous and highly nonlinear stochastic differential delay equations

This paper focuses on the strong convergence of the truncated $θ$-Milstein method for a class of nonautonomous stochastic differential delay equations whose drift and diffusion coefficients can grow polynomially. The convergence rate, which is close to one, is given under the weaker assumption than the monotone condition. To verify our theoretical findings, we present a numerical example.

随机延迟微分方程数值方法的均方指数稳定性

Mean square exponential stability of numerical methods for stochastic differential delay equations

本文研究随机延迟微分方程的θ-EM和MTEM数值方法的均方指数稳定性，提出新判据，并用两个例子验证。

部分截断的欧拉-马尔可夫方法用于具有可变延迟和马尔可夫切换的超线性随机延迟微分方程

The Partially Truncated Euler-Maruyama Method for super-linear Stochastic Delay Differential Equations with variable delay and Markovian switching

本文研究了一类具有可变延迟和马尔可夫切换的超线性随机延迟微分方程，提出了一种部分截断的欧拉-马尔可夫方法，并探讨了在广义Khasminskii型条件下的数值解收敛性和稳定性特性。

Logarithmic Euler Maruyama Scheme for Multi Dimensional Stochastic Delay Differential Equation

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 scheme always maintains positivity subject to initial conditions. We then show the convergence of the proposed Euler-Maruyama scheme. With this scheme, all the approximate solutions are positive and the rate of convergence of this scheme is 0.5.