论文标题
蒙特卡洛估计分数部分微分方程的溶液
Monte Carlo estimation of the solution of fractional partial differential equations
论文作者
论文摘要
该论文是基于其概率解释的分数PDE的数值解，即，我们通过某些蒙特卡洛模拟构建近似解决方案。主要结果代表了精确溶液和蒙特卡洛近似之间的误差的上限，通过适当的中心极限定理（CLT）的波动估计以及置信区间的构建。此外，我们通过Berry-Esseen类型边界提供CLT中的收敛速度。包括具体的数值计算和插图。
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.
