| 带Poisson跳和Markovian调制的中立型随机延迟微分方程的数值解的收敛性 |
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| 引用本文： | 岑利群,周少波.带Poisson跳和Markovian调制的中立型随机延迟微分方程的数值解的收敛性[J].应用数学,2010,23(1). |
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| 作者姓名： | 岑利群 周少波 |
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| 作者单位： | 华中科技大学数学与统计学院,湖北,武汉,430074 |
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| 摘 要： | 本文研究带Poisson跳和Markovian调制的中立型随机微分方程的数值解的收敛性质.用数值逼近方法求此微分方程的解,并证明了Euler近似解在此线性增长条件和全局Lipschitz条件更弱的条件下仍均方收敛于此方程的解析解.
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| 关 键 词： | Poisson跳 Euler-Maruyama方法 Markovian调制 局部Lipschitz条件 |
Convergence of Numerical Solutions to Neutral Stochastic Delay Differential Equation with Poisson Jump and Markovian Switching |
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| CEN Li-qun,ZHOU Shao-bo.Convergence of Numerical Solutions to Neutral Stochastic Delay Differential Equation with Poisson Jump and Markovian Switching[J].Mathematica Applicata,2010,23(1). |
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| Authors: | CEN Li-qun ZHOU Shao-bo |
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| Abstract: | The main purpose of this paper is to study the convergence of numerical solutions to a class of neutral stochastic delay differential equations with Poisson jump and Markovian switching.A numerical approximation scheme is proposed to approximate the solutions to neutral stochastic delay differential equations with Poisson jump and Markovian switching. It is proved that the Euler approximation solutions converge to the analytic solutions in the mean square under weaker conditions than the linear growth conditions and global Lipschitz conditions. |
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| Keywords: | Poisson jump Euler-Maruyama method Markovian switching Local Lipschitz condition |
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