THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

α=0时, 该方程退化为非线性随机微分方程, 所获结论与现有文献中的相关结论是一致的; 当α ≠ 0, 且初值条件为齐次时, 所获结论可视为现有文献中线性随机分数阶微分方程情形的推广和改进. 随后, 文末的数值试验验证了所获理论结果的正确性.","endNoteUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/article/getTxtFile.do?fileType=EndNote&id=48640","reference":"[1] Anh V V, Mcvinish R. Fractional differential equations driven by Lévy noise[J]. J. Appl. Math. Stoch. Anal., 2003, 16(2):97-119.
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[20] 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.","bibtexUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/article/getTxtFile.do?fileType=BibTeX&id=48640","abstractUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/10.12286/jssx.j2019-0587","qi":"1","id":48640,"nian":2021,"bianHao":"1612405295414-231758780","zuoZheEn_L":"Zhu Mengjiao, Wang Wenqiang","juanUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/Y2021","qiShiYe":"87","received":"2019-04-18","qiUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/Y2021/V43/I1","lanMu_cn":"论文","pdfSize":"533","zuoZhe_CN":"朱梦姣, 王文强","risUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/article/getTxtFile.do?fileType=Ris&id=48640","title_cn":"非线性随机分数阶微分方程Euler方法的弱收敛性","doi":"10.12286/jssx.j2019-0587","jieShuYe":"109","keywordList_en":["Nonlinear stochastic fractional differential equations","Existence and uniqueness of solutions","Euler method","Weak convergence","Caputo derivative"],"endNoteUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/article/getTxtFile.do?fileType=EndNote&id=48640","zhaiyao_en":"This paper is concerned with the existence and uniqueness of solutions for nonlinear stochastic fractional differential equations and the weak convergence of Euler method constructed for solving the equations when they satisfy certain constraints. Especially, when fractional order α = 0, the equations are degenerated to nonlinear stochastic differential equations, and the conclusions obtained from this paper are consisted with the relevant results; when α ≠ 0 and the initial condition is homogeneous, the conclusions can be regarded as the generalization and improvement of linear stochastic fractional differential equations in the existing literature. Finally, numerical examples illustrate the effectiveness of the theoretical results.","bibtexUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/article/getTxtFile.do?fileType=BibTeX&id=48640","abstractUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/10.12286/jssx.j2019-0587","zuoZheCn_L":"朱梦姣, 王文强","juanUrl_cn":"https://chinamath.cjoe.ac.cn/qkw/jssx/CN/Y2021","lanMu_en":"","qiUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/Y2021/V43/I1","zuoZhe_EN":"Zhu Mengjiao, Wang Wenqiang","risUrl_en":"https://chinamath.cjoe.ac.cn/qkw/jssx/EN/article/getTxtFile.do?fileType=Ris&id=48640","title_en":"THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS","hasPdf":"true"}}"/>

THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

Zhu Mengjiao, Wang Wenqiang

Mathematica Numerica Sinica ›› 2021, Vol. 43 ›› Issue (1) : 87-109.

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中国科学院数学与系统科学研究院期刊网

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Mathematica Numerica Sinica ›› 2021, Vol. 43 ›› Issue (1) : 87-109. DOI: 10.12286/jssx.j2019-0587

THE WEAK CONVERGENCE OF EULER METHOD FOR NONLINEAR STOCHASTIC FRACTIONAL DIFFERENTIAL EQUATIONS

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{{article.zuoZheEn_L}}. {{article.title_en}}. Mathematica Numerica Sinica, 2021, 43(1): 87-109 https://doi.org/10.12286/jssx.j2019-0587

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