共查询到17条相似文献,搜索用时 93 毫秒
1.
2.
3.
4.
5.
本文研究了数值求解非自治随机微分方程的正则Euler-Maruyama分裂(CEMS)方法,该方程的漂移项系数带有刚性且允许超线性增长,扩散项系数满足全局Lipschitz条件.首先,证明了CEMS方法的强收敛性及收敛速度.其次,证明了在适当条件下CEMS方法是均方稳定的.进一步,利用离散半鞅收敛定理,研究了CEMS方法的几乎必然指数稳定性.结果表明,CEMS方法在漂移系数的刚性部分满足单边Lipschitz条件下可保持几乎必然指数稳定性.最后通过数值实验,检验了CEMS方法的有效性并证实了我们的理论结果. 相似文献
6.
7.
8.
9.
10.
给出了一类带时滞随机种群系统,通过Ito公式,在局部Lipschitz条件和广义Khasminskii-type条件下.运用Euler-Maruyama法讨论了带时滞随机种群系统数值解,并给出了渐进估计,通过数值算例对主要结果进行验证. 相似文献
11.
In this paper, we consider strong convergence and almost sure exponential stability of the backward Euler-Maruyama method for nonlinear hybrid stochastic differential equations with time-variable delay. Under the local Lipschitz condition and polynomial growth condition, it is proved that the backward Euler-Maruyama method is strongly convergent. Additionally, the moment estimates and almost sure exponential stability for the analytical solution are proved. Also, under the appropriate condition, we show that the numerical solutions for the backward Euler-Maruyama methods are almost surely exponentially stable. A numerical experiment is given to illustrate the computational effectiveness and the theoretical results of the method. 相似文献
12.
Wei Zhang 《计算数学(英文版)》2022,40(4):607-623
In this paper, we consider the Euler-Maruyama method for a class of stochastic Volterra integral equations (SVIEs). It is known that the strong convergence order of the Euler-Maruyama method is $\frac12$. However, the strong superconvergence order $1$ can be obtained for a class of SVIEs if the kernels $\sigma_{i}(t, t) = 0$ for $i=1$ and $2$; otherwise, the strong convergence order is $\frac12$. Moreover, the theoretical results are illustrated by some numerical examples. 相似文献
13.
Exponential stability of Euler-Maruyama solutions for impulsive stochastic differential equations with delay 总被引:1,自引:0,他引:1
This paper establishes a method to study the exponential stability of Euler-Maruyama (EM) method for impulsive stochastic differential equations with delay. By using the properties of M-matrix and stochastic analysis technique, some conditions under which the EM solution is exponentially mean-square stable are obtained. Some examples are provided to illustrate the results. 相似文献
14.
Siyuan Qi & Guangqiang Lan 《计算数学(英文版)》2022,40(3):437-452
We consider a nonlinear stochastic Volterra integral equation with time-dependent delay and the corresponding Euler-Maruyama method in this paper. Strong convergence rate (at fixed point) of the corresponding Euler-Maruyama method is obtained when coefficients $f$ and $g$ both satisfy local Lipschitz and linear growth conditions. An example is provided to interpret our conclusions. Our result generalizes and improves the conclusion in [J. Gao, H. Liang, S. Ma, Strong convergence of the semi-implicit Euler method for nonlinear stochastic Volterra integral equations with constant delay, Appl. Math. Comput., 348 (2019) 385-398.] 相似文献
15.
Wei Zhang 《计算数学(英文版)》2020,38(6):903-932
The key aim of this paper is to show the strong convergence of the truncated Euler-Maruyama method for neutral stochastic differential delay equations (NSDDEs) with
Markovian switching (MS) without the linear growth condition. We present the truncated Euler-Maruyama method of NSDDEs-MS and consider its moment boundedness under
the local Lipschitz condition plus Khasminskii-type condition. We also study its strong
convergence rates at time $T$ and over a finite interval $[0, T]$. Some numerical examples are
given to illustrate the theoretical results. 相似文献
16.
In this paper, we develop the truncated Euler-Maruyama (EM) method for
stochastic differential equations with piecewise continuous arguments (SDEPCAs),
and consider the strong convergence theory under the local Lipschitz condition plus
the Khasminskii-type condition. The order of convergence is obtained. Moreover,
we show that the truncated EM method can preserve the exponential mean square
stability of SDEPCAs. Numerical examples are provided to support our conclusions. 相似文献
17.
The Balanced method was introduced as a class of quasi-implicit methods, based upon the Euler-Maruyama scheme, for solving stiff stochastic differential equations. We extend the Balanced method to introduce a class of stable strong order 1.0 numerical schemes for solving stochastic ordinary differential equations. We derive convergence results for this class of numerical schemes. We illustrate the asymptotic stability of this class of schemes is illustrated and is compared with contemporary schemes of strong order 1.0. We present some evidence on parametric selection with respect to minimising the error convergence terms. Furthermore we provide a convergence result for general Balanced style schemes of higher orders. 相似文献