椭圆与亚椭圆扩散的反多级方法及其应用
Antithetic Multilevel Methods for Elliptic and Hypo-Elliptic Diffusions with Applications
AI总结：
提出一种无需 Lévy 区域模拟且具有 2 阶强误差和 2 阶弱误差的新型反多级蒙特卡洛方法，用于估计椭圆或亚椭圆扩散过程期望，并证明其在部分观测扩散滤波等问题中相较现有方法具有显著效率提升。
摘要：
我们提出了一种新的反多级蒙特卡洛（MLMC）方法，用于估计关于椭圆或亚椭圆扩散过程定律的期望。特别地，我们考虑必须对扩散进行时间离散化和对此类方案进行数值模拟的情况。受近期工作的启发，我们引入了一种新的期望 MLMC 估计器，它不需要任何 Lévy 区域模拟，具有 2 阶强误差和 2 阶弱误差。然后我们展示了如何将这种方法应用于具有离散时间观测的部分观测扩散相关的滤波问题中。我们通过数值模拟说明，相对于一些现有方法，我们的新方法在多个问题上提供了效率提升，特别是当扩散过程为亚椭圆时。
英文摘要：
We present a new antithetic multilevel Monte Carlo (MLMC) method for the estimation of expectations with respect to laws of diffusion processes that can be elliptic or hypo-elliptic. In particular, we consider the case where one has to resort to time discretization of the diffusion and numerical simulation of such schemes. Inspired by recent works, we introduce a new MLMC estimator of expectations, which does not require any Lévy area simulation and has a strong error of order 2 and a weak error of order 2. We then show how this approach can be used in the context of the filtering problem associated to partially observed diffusions with discrete time observations. We illustrate that in numerical simulations our new approaches provide efficiency gains for several problems, particularly when the diffusion process is hypo-elliptic, relative to some existing methods.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
