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

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α_m-α_m-1，其中α_i为分数阶导数的指标，且满足0<α₁<…<α_m-1<α_m<1.最后，通过数值实验验证了理论分析结果的正确性.

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

A modified Euler-Maruyama (EM) scheme was constructed for a class of multi-term fractional nonlinear stochastic differential equations with weak singularity kernels, and the strong convergence of this modified EM scheme was proved. Specifically, according to the sufficient condition for stochastic integral decomposition, the multi-term fractional stochastic differential equation was equivalently transformed into the stochastic Volterra integral equation, and then the corresponding modified EM scheme and its strong convergence were derived and proved, respectively. The order of strong convergence is α_m-α_m-1, where α_i is the index of fractional derivative satisfying 0<α₁<…<α_m-1<α_m<1. Finally, numerical experiments verify the correctness of the theoretical results.