Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations
Well-posedness and EM approximations for non-Lipschitz stochastic fractional integro-differential equations
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非 Lipschitz 随机分数阶积分微分方程的适定性和 EM 近似
DOI：
10.1016/j.cam.2019.02.002
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发表时间：
2019
影响因子：
2.4
通讯作者：
Xiao Aiguo
中科院分区：
文献类型：
--
作者：
Dai Xinjie;Bu Weiping;Xiao Aiguo
本文研究了非lipschitz条件下的非线性随机分数阶积分微分方程（sfids），它是一般的，包含了许多文献中讨论过的随机分数阶积分微分方程。利用傅比尼定理，详细推导了sfids与随机Volterra积分方程之间的重要联系。利用Euler-Maruyama （EM）逼近，证明了该类问题解的存在性、唯一性和稳定性。此外，还证明了改进的sides EM解具有强的一阶锐收敛性。算例表明了数值格式的准确性和有效性，验证了理论分析的正确性。
This paper considers the nonlinear stochastic fractional integro-differential equations (SFIDEs) under the non-Lipschitz conditions, which are general and include many stochastic (fractional) integro-differential equations discussed in literature. An important connection between SFIDEs and stochastic Volterra integral equations (SVIEs) is derived in detail by the Fubini theorem. Using the Euler–Maruyama (EM) approximation, we prove the existence, uniqueness and stability results of the solution to SFIDEs. Moreover, it is shown that the modified EM solution of SFIDEs shares strong first-order sharp convergence. The numerical examples are performed to show the accuracy and effectiveness of the numerical scheme and verify the correctness of our theoretical analysis.