带有弱奇性核的多项分数阶非线性随机微分方程解的适定性  

Well-Posedness of Solutions of Multi-Term Fractional Nonlinear Stochastic Differential Equations with Weakly Singular Kernel

作　　者：黄健飞 钱思颖 张静娜 HUANG Jianfei;QIAN Siying;ZHANG Jingna(College of Mathematical Sciences,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,扬州225002

出　　处：《应用数学学报》2023年第2期196-210,共15页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11701502,11871065);江苏省自然科学基金资助项目(BK20201427)。

摘　　要：本文主要研究一类带有多项分数阶Caputo导数的非线性随机微分方程初值问题的解的适定性.具体地,首先把多项分数阶随机微分方程等价地转化为随机Volterra积分方程;然后,给出了该随机积分方程的Euler-Maruyama(EM)格式;最后,借助于该EM格式,证明了多项分数阶随机微分方程的解的适定性.In this paper,we study the well-posedness of solutions of a class of nonlinear stochastic differential equations with multi-term fractional Caputo derivatives.Specifically,firstly,the multi-term fractional stochastic differential equation is equivalently transformed into stochastic Volterra integral equation.Then,the Euler-Maruyama(EM)scheme of the stochastic integral equation is given.Finally,by using the EM scheme,the well-posedness of the solution of the multi-term fractional stochastic differential equation is proved.

关 键 词：分数阶随机微分方程 弱奇性核 多项分数阶微积分 Euler-Maruyama格式 解的适定性 

分 类 号：O211.9[理学—概率论与数理统计]