Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Multilevel Monte Carlo method for parabolic stochastic partial differential equations
复制标题
抛物型随机偏微分方程的多级蒙特卡罗方法
DOI：
10.1007/s10543-012-0401-5
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发表时间：
2013
影响因子：
1.5
通讯作者：
C. Schwab
中科院分区：
文献类型：
--
作者：
A. Barth;A. Lang;C. Schwab
我们分析了由平方集成型驱动的一类抽象随机，抛物线方程的多级蒙特卡洛离散性的收敛性和复杂性。玛鲁山的离散化时间在空间中的均方一体收敛和1/2阶的均值收敛到温和溶液的预期值。多级估计量的复杂性与相应的工作相对于相应的网格的单个路径，在最佳的确定性抛物线问题上。
We analyze the convergence and complexity of multilevel Monte Carlo discretizations of a class of abstract stochastic, parabolic equations driven by square integrable martingales. We show under low regularity assumptions on the solution that the judicious combination of low order Galerkin discretizations in space and an Euler–Maruyama discretization in time yields mean square convergence of order one in space and of order 1/2 in time to the expected value of the mild solution. The complexity of the multilevel estimator is shown to scale log-linearly with respect to the corresponding work to generate a single path of the solution on the finest mesh, resp. of the corresponding deterministic parabolic problem on the finest mesh.
影响因子：
2.7
作者：
Giles, Michael B.
通讯作者：
Giles, Michael B.
影响因子：
2.1
作者：
Barth, Andrea;Schwab, Christoph;Zollinger, Nathaniel
通讯作者：
Zollinger, Nathaniel