A random walk-based method is proposed to efficiently compute the solution of a large class of fractional in time linear systems of differential equations (linear F-ODE systems), along with the derivatives with respect to the system parameters. Such a method is unbiased and unconditionally stable, and can therefore be used to provide an unbiased estimation of individual entries of the solution, or the full solution. By using stochastic differentiation techniques, it can be used as well to provide unbiased estimators of the sensitivities of the solution with respect to the problem parameters without any additional computational cost. The time complexity of the algorithm is discussed here, along with suitable variance bounds, which prove in practice the convergence of the algorithm. Finally, several test cases were run to assess the validity of the algorithm.

翻译：本文提出了一种基于随机游走的方法，用于高效计算一大类分数阶时间线性微分方程组（线性F-ODE系统）的解及其对系统参数的导数。该方法具有无偏性和无条件稳定性，因此可用于提供解的单个分量或完整解的无偏估计。通过采用随机微分技术，该方法还能在不增加额外计算成本的前提下，提供解关于问题参数灵敏度的无偏估计量。本文讨论了算法的时间复杂度及合适的方差界，从实践角度证明了算法的收敛性。最后，通过多个测试案例验证了算法的有效性。