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带有弱奇性核的多项分数阶非线性随机微分方程的改进Euler-Maruyama格式

钱思颖 张静娜 黄健飞

钱思颖, 张静娜, 黄健飞. 带有弱奇性核的多项分数阶非线性随机微分方程的改进Euler-Maruyama格式[J]. 应用数学和力学, 2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067
引用本文: 钱思颖, 张静娜, 黄健飞. 带有弱奇性核的多项分数阶非线性随机微分方程的改进Euler-Maruyama格式[J]. 应用数学和力学, 2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067
QIAN Siying, ZHANG Jingna, HUANG Jianfei. A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067
Citation: QIAN Siying, ZHANG Jingna, HUANG Jianfei. A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels[J]. Applied Mathematics and Mechanics, 2021, 42(11): 1203-1212. doi: 10.21656/1000-0887.420067

带有弱奇性核的多项分数阶非线性随机微分方程的改进Euler-Maruyama格式

doi: 10.21656/1000-0887.420067
基金项目: 

江苏省自然科学基金(BK20201427);国家自然科学基金(11701502;11871065)

详细信息
    作者简介:

    钱思颖(1995—),男,硕士生(E-mail: 17865676836@163.com);黄健飞(1983—),男,副教授,博士(通讯作者. E-mail: jfhuang@lsec.cc.ac.cn).

    通讯作者:

    黄健飞(1983—),男,副教授,博士(通讯作者. E-mail: jfhuang@lsec.cc.ac.cn).

  • 中图分类号: O211.5|O241.8

A Modified Euler-Maruyama Scheme for Multi-Term Fractional Nonlinear Stochastic Differential Equations With Weakly Singular Kernels

Funds: 

The National Natural Science Foundation of China(11701502;11871065)

  • 摘要: 针对一类带有弱奇性核的多项分数阶非线性随机微分方程构造了改进Euler-Maruyama (EM)格式,并证明了该格式的强收敛性.具体地,利用随机积分解的充分条件,将此多项分数阶随机微分方程等价地转化为随机Volterra 积分方程的形式,详细推导出对应的改进EM格式,并对该格式进行了强收敛性分析,其强收敛阶为αmm-1,其中αi为分数阶导数的指标,且满足0<α1<…<αm-1m<1.最后,通过数值实验验证了理论分析结果的正确性.
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出版历程
  • 收稿日期:  2021-03-15
  • 修回日期:  2021-04-26
  • 网络出版日期:  2021-12-07

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