论文标题
$σ$ - 安静的多级蒙特卡洛法的中央限制定理
Central Limit Theorem for the $σ$-antithetic multilevel Monte Carlo method
论文作者
论文摘要
在本文中，我们介绍了$σ$ - 安排多级蒙特卡洛（MLMC）估计器，以进行多维扩散，这是由Giles和Szpruch \ cite {a}引入的原始抗心性MLMC的扩展版本。我们的目的是研究这种新算法所涉及的弱错误的渐近行为。 Among the obtained results, we prove that the error between on the one hand the average of the Milstein scheme without Lévy area and its $σ$-antithetic version build on the finer grid and on the other hand the coarse approximation stably converges in distribution with a rate of order 1. We also prove that the error between the Milstein scheme without Lévy area and its $σ$-antithetic version stably converges in distribution with a rate of order $1/2$.更确切地说，我们基于三角阵列方法的连接分布的分布的渐近行为具有功能限制定理（例如，参见Jacod \ cite \ cite {c}）。得益于此结果，我们为$σ$ - 安静的MLMC估计器建立了Lindeberg-Feller类型的中心限制定理。执行算法的时间复杂性。
In this paper, we introduce the $σ$-antithetic multilevel Monte Carlo (MLMC) estimator for a multi-dimensional diffusion which is an extended version of the original antithetic MLMC one introduced by Giles and Szpruch \cite{a}. Our aim is to study the asymptotic behavior of the weak errors involved in this new algorithm. Among the obtained results, we prove that the error between on the one hand the average of the Milstein scheme without Lévy area and its $σ$-antithetic version build on the finer grid and on the other hand the coarse approximation stably converges in distribution with a rate of order 1. We also prove that the error between the Milstein scheme without Lévy area and its $σ$-antithetic version stably converges in distribution with a rate of order $1/2$. More precisely, we have a functional limit theorem on the asymptotic behavior of the joined distribution of these errors based on a triangular array approach (see e.g. Jacod \cite{c}). Thanks to this result, we establish a central limit theorem of Lindeberg-Feller type for the $σ$-antithetic MLMC estimator. The time complexity of the algorithm is carried out.
