带Caputo导数的变分数阶随机微分方程的Euler-Maruyama方法

An Euler⁃Maruyama Method for Variable Fractional StochasticDifferential Equations With Caputo Derivatives

该文构造了Euler-Maruyama(EM)方法求解一类带Caputo导数的变分数阶随机微分方程.首先,证明了该方程的适定性;然后,详细推导出对应的EM方法,并对该方法进行了强收敛性的分析,通过使用EM方法的连续形式证明了其强收敛阶为β-0.5,其中β是Caputo导数的阶数,且满足0.5<β<1.最后,通过数值实验验证了理论分析结果的正确性.

A Euler⁃Maruyama(EM)method was constructed to solve a class of variable fractional stochastic differential equations with Caputo derivatives.Firstly,the well⁃posedness of the equation was proved.Then,the corresponding EM method was derived in detail,and the strong convergence of the method was analyzed.By means of the continuous form of the EM method,its strong convergence order was proved to beβ-0.5,whereβis the order of the Caputo derivative and 0.5<β<1.Numerical experiments verify the correctness of the theoretical results.