A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes
A Note on the Importance of Weak Convergence Rates for SPDE Approximations in Multilevel Monte Carlo Schemes
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DOI：
10.1007/978-3-319-33507-0_25
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发表时间：
2015-08
期刊：
影响因子：
--
通讯作者：
A. Lang
中科院分区：
文献类型：
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作者：
A. Lang
这是一个众所周知的 随机偏微分方程近似的弱收敛阶实质上是相应的强收敛阶的两倍。这是已知的许多近似的随机（常）微分方程，而它是最近的研究随机偏微分方程。在这份说明中，它是如何的可用性弱收敛结果影响的样本数在多级Monte Carlo计划，从而降低了计算复杂性，这些计划的近似的一个给定的精度。
It is a well-known rule of thumb that approximations of stochastic partial differential equations have essentially twice the order of weak convergence compared to the corresponding order of strong convergence. This is already known for many approximations of stochastic (ordinary) differential equations while it is recent research for stochastic partial differential equations. In this note it is shown how the availability of weak convergence results influences the number of samples in multilevel Monte Carlo schemes and therefore reduces the computational complexity of these schemes for a given accuracy of the approximations.