The paper is devoted to the numerical solutions of fractional PDEs based on its probabilistic interpretation, that is, we construct approximate solutions via certain Monte Carlo simulations. The main results represent the upper bound of errors between the exact solution and the Monte Carlo approximation, the estimate of the fluctuation via the appropriate central limit theorem (CLT) and the construction of confidence intervals. Moreover, we provide rates of convergence in the CLT via Berry-Esseen type bounds. Concrete numerical computations and illustrations are included.

中文翻译：

---

分数阶偏微分方程解的蒙特卡洛估计

本文基于其概率解释，致力于分数PDE的数值解，即，我们通过某些Monte Carlo模拟构造近似解。主要结果表示精确解与蒙特卡洛近似之间的误差上限，通过适当的中心极限定理（CLT）估计波动以及建立置信区间。此外，我们通过Berry-Esseen类型界限提供了CLT中的收敛速率。包括具体的数值计算和图示。