共查询到20条相似文献,搜索用时 15 毫秒
1.
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
2.
本文研究非线性中立型随机延迟微分方程随机θ方法的均方稳定性.在方程解析解均方稳定的条件下,证明了如下结论:当θ∈[0,1/2)时,随机θ方法对于适当小的时间步长是均方稳定的;当θ∈[1/2,1]时,随机θ方法对于任意步长都是均方稳定的.数值结果验证了所获结论的正确性. 相似文献
3.
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
4.
Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels 下载免费PDF全文
We propose a generalized Jacobi spectral-Galerkin method for the nonlinear
Volterra integral equations (VIEs) with weakly singular kernels. We establish the
existence and uniqueness of the numerical solution, and characterize the convergence
of the proposed method under reasonable assumptions on the nonlinearity. We also
present numerical results which are consistent with the theoretical predictions. 相似文献
5.
Chaman Kumar 《随机分析与应用》2013,31(2):207-228
The strong convergence of Euler approximations of stochastic delay differential equations is proved under general conditions. The assumptions on drift and diffusion coefficients have been relaxed to include polynomial growth and only continuity in the arguments corresponding to delays. Furthermore, the rate of convergence is obtained under one-sided and polynomial Lipschitz conditions. Finally, our findings are demonstrated with the help of numerical simulations. 相似文献
6.
In this paper, we consider the stochastic differential equations with piecewise continuous arguments (SDEPCAs) in which the drift coefficient satisfies the generalized one-sided Lipschitz condition and the diffusion coefficient satisfies the linear growth condition. Since the delay term $t-[t]$ of SDEPCAs is not continuous and differentiable, the variable substitution method is not suitable. To overcome this difficulty, we adopt new techniques to prove the boundedness of the exact solution and the numerical solution. It is proved that the truncated Euler-Maruyama method is strongly convergent to SDEPCAs in the sense of $L^{\bar{q}}(\bar{q}\ge 2)$. We obtain the convergence order with some additional conditions. An example is presented to illustrate the analytical theory. 相似文献
7.
我们主要构造了数值求解一类1指标随机延迟微分代数系统的Euler-Maruyama方法,并且证明用该方法求解此类问题可达到1/2阶均方收敛.最后的效值试验验证了方法的有效性及所获结论的正确性. 相似文献
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This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented. 相似文献
10.
This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations (SDDEs) of Itô-type. The method is proved to be mean-square convergent of order min{$1/2, \hat{p}$} under the Lipschitz condition and the linear growth condition, where $\hat{p}$ is the exponent of Hölder condition of the initial function. Stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter $p$ the derived method can have a better stability property than more commonly used numerical methods. That is, for some $p$, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters $p$. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient. 相似文献
11.
本文借助星型Mobius反演得到随机积分Volterra方程的一个全新解法.它旨在揭示离散反演与连续反演的内在联系,为探索各类反演的统一性提供了一种可能的研究途径. 相似文献
12.
Spline Collocation-Interpolation Method for Linear and Nonlinear Cordial Volterra Integral Equations
Gennadi Vainikko 《Numerical Functional Analysis & Optimization》2013,34(1):83-109
We study the convergence and convergence speed of the discontinuous spline collocation and collocation-interpolation methods on uniform grids for linear and nonlinear Volterra integral equations of the second kind with noncompact operators. 相似文献
13.
本文针对一般的非线性随机延迟微分方程,证明了当系统理论解满足均方稳定性条件时,则当方程的漂移和扩散项满足一定的条件时,Milstein方法也是均方稳定的.数学实验进一步验证了我们的结论. 相似文献
14.
Abstract In this article the numerical approximation of solutions of Itô stochastic delay differential equations is considered. We construct stochastic linear multi-step Maruyama methods and develop the fundamental numerical analysis concerning their 𝕃 p -consistency, numerical 𝕃 p -stability and 𝕃 p -convergence. For the special case of two-step Maruyama schemes we derive conditions guaranteeing their mean-square consistency. 相似文献
15.
该文的主要目的是通过使用Legendre配置方法和正则化策略来求解带有噪声数据的第一类Volterra积分方程,并给出该方法收敛性分析的严格数学证明.数值实验表明了该方法的有效性. 相似文献
16.
提出了随机微分方程的离散型波形松弛方法,证明了它是几乎必然收敛的.此外,通过数值实验验证了所得结果. 相似文献
17.
Haiyan Yuan 《计算数学(英文版)》2022,40(2):177-204
In this paper, the numerical methods for semi-linear stochastic delay integro-differential equations are studied. The uniqueness, existence and stability of analytic solutions of semi-linear stochastic delay integro-differential equations are studied and some suitable conditions for the mean-square stability of the analytic solutions are also obtained. Then the numerical approximation of exponential Euler method for semi-linear stochastic delay integro-differential equations is constructed and the convergence and the stability of the numerical method are studied. It is proved that the exponential Euler method is convergent with strong order $\frac{1}{2}$ and can keep the mean-square exponential stability of the analytical solutions under some restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results. 相似文献
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利用一个新的不动点定理在较弱的条件下考虑Banach空间中一类非线性Voherra型积分方程整体解的存在性.由于非线性项中含有非线性积分算子,相对于线性积分算子,文章所得结论推广并丰富了已有文献的一些结果. 相似文献
20.
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. 相似文献