| 带有Poisson随机测度的比例微分方程数值解的收敛性 |
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| 引用本文： | 毛伟,韩修静.带有Poisson随机测度的比例微分方程数值解的收敛性[J].大学数学,2010,26(2). |
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| 作者姓名： | 毛伟 韩修静 |
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| 作者单位： | 1. 江苏教育学院,数学系,江苏,南京,210013
2. 江苏大学,理学院,江苏,镇江,212013 |
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| 基金项目： | 江苏教育学院重点课题 |
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| 摘 要： | 主要研究了带跳的随机比例微分方程dX(t)=f((X(t),X(qt))dt+g(X(t),X(qt))dW(t)+∫nh(X(t),X(qt),u)N(dt,du),0≤t≤T,X(0)=X0,给出了此方程的Euler数值解,并在局部Lipschitzs条件下,证明了数值解依均方和概率测度意义下收敛于精确解.
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| 关 键 词： | 随机比例微分方程 补偿Poisson随机测度 Euler方法 数值解 L2收敛和依概率测度收敛 |
Convergence of Numerical Solutions for Pantograph Equations with Poisson Random Measure |
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| MAO Wei,HAN Xiu-jing.Convergence of Numerical Solutions for Pantograph Equations with Poisson Random Measure[J].College Mathematics,2010,26(2). |
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| Authors: | MAO Wei HAN Xiu-jing |
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| Abstract: | We mainly study the following stochastic pantograph equations with jumps(SPEwJs):dX(t)=f(X(t),X(qt)dt+g(X(t),X(qt))dW(t)+∫nh(X(t),X(qt),u)(dt,du),0≤t≤T,X(0)=X0,The Euler approximate solution for SPEwJs is established,under the local Lipschitzs condition,we prove that the numerical solution converges to the analytical solution in L2 sense as well as in probability sense. |
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| Keywords: | stochastic pantograph equations compensated Poisson random measure Euler method numerical solution convergence in L2 and in probability |
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