| 一类带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性 |
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| 引用本文： | 毛文亭,王文强,林伟贤.一类带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性[J].计算数学,2016,38(4):442-452. |
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| 作者姓名： | 毛文亭 王文强 林伟贤 |
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| 作者单位： | 湘潭大学数学与计算科学学院, 湖南湘潭 411105 |
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| 基金项目： | 国家自然科学基金(11571373;11671343)和湖南省教育厅重点项目(14A146)资助项目 |
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| 摘 要： | 本文主要在带加性噪声随机分数阶微分方程的基础上,研究了一类更为困难的带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性,并得到了类似的结论.首先构造了数值求解带乘性噪声随机分数阶微分方程的Euler方法,然后证明当分数阶α满足0α1/2时,该方法是1/2-α阶弱收敛的和弱稳定的,文末数值试验的结果验证了理论结果的正确性.
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| 关 键 词： | 带乘性噪声随机分数阶微分方程 Euler方法 弱收敛性 弱稳定性 |
| 收稿时间： | 2016-04-22; |
WEAK CONVERGENCE AND WEAK STABILITY OF EULER METHOD FOR A CLASS OF STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION WITH MULTIPLICATIVE NOISE |
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| Mao Wenting,Wang Wenqiang,Lin Weixian.WEAK CONVERGENCE AND WEAK STABILITY OF EULER METHOD FOR A CLASS OF STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION WITH MULTIPLICATIVE NOISE[J].Mathematica Numerica Sinica,2016,38(4):442-452. |
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| Authors: | Mao Wenting Wang Wenqiang Lin Weixian |
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| Institution: | School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, Hunan, China |
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| Abstract: | Based on the stochastic fractional differential equation with additive noise, this paper studied the weak convergence and weak stability of Euler method for a class of stochastic fractional differential equation with multiplicative noise, and a similar conclusion is obtained as well. Firstly, the Euler method was constructed to solve the stochastic fractional differential equation with multiplicative noise, and then it was proved that the method was 1/2-α-order weak convergence and weak stability when the fractional order α satisfy 0< α< 1/2. Finally, one numerical example is given. The theoretical results are also confirmed by a numerical experiment. |
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| Keywords: | stochastic fractional differential equation with multiplicative noise Euler method weak convergence weak stability |
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