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

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.