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一类带乘性噪声随机分数阶微分方程数值方法的弱收敛性与弱稳定性

毛文亭, 张维, 王文强   

  1. 湘潭大学数学与计算科学学院, 湘潭 411105
  • 收稿日期:2017-03-10 出版日期:2018-09-15 发布日期:2018-09-10
  • 基金资助:

    国家自然科学基金(11271311,11171352)和湖南省教育厅重点项目(14A146)资助项目.

毛文亭, 张维, 王文强. 一类带乘性噪声随机分数阶微分方程数值方法的弱收敛性与弱稳定性[J]. 数值计算与计算机应用, 2018, 39(3): 161-171.

Mao Wenting, Zhang Wei, Wang Wenqiang. WEAK CONVERGENCE AND WEAK STABILITY OF A NUMERICAL METHOD FOR THE CLASS OF STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION WITH MULTIPLICATIVE NOISE[J]. Journal of Numerical Methods and Computer Applications, 2018, 39(3): 161-171.

WEAK CONVERGENCE AND WEAK STABILITY OF A NUMERICAL METHOD FOR THE CLASS OF STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATION WITH MULTIPLICATIVE NOISE

Mao Wenting, Zhang Wei, Wang Wenqiang   

  1. School of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
  • Received:2017-03-10 Online:2018-09-15 Published:2018-09-10
本文研究了一类带乘性噪声随机分数阶微分方程数值方法的弱收敛性和弱稳定性.首先基于Itô公式和Riemann-Liouville分数阶导数构造了求解带乘性噪声随机分数阶微分方程的数值方法,然后证明当分数阶α满足0 < α < 1时,该方法是1-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.
This paper investigates the weak convergence and weak stability of the numerical method for a class of stochastic fractional differential equation with multiplicative noise. Firstly, the numerical method which is used to solve the stochastic fractional differential equation with multiplicative noise, is constructed by Itô formula and Riemann-Liouville fractional derivative. Then it is proved that the method is 1 -α order weak converges and weak stable when the fractional order α satisfy 0 < α < 1. Finally, one numerical example is given. The theoretical results are also confirmed by a numerical experiment.

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