论文标题
在小噪声渐近学中以蒙特卡洛分裂的罕见事件模拟的波动
Fluctuations of Rare Event Simulation with Monte Carlo Splitting in the Small Noise Asymptotics
论文作者
论文摘要
考虑到噪声小噪声以达到目标集的条件的扩散过程。 AMS算法是一种蒙特卡洛方法，用于通过迭代模拟该过程的克隆并选择已达到所谓重要性函数的最高值的轨迹来采样此类罕见事件。在本文中，考虑了AMS的较大样本量相对差异。主要结果是在小噪声渐近学中，后者的偏差对数等效，这是严格衍生的。它是根据与潜在的小噪声大偏差相关的准电位成本函数明确表示的最大化问题。提供了必要和足够的几何条件，以确保获得所获得数量的消失（“弱”渐近效率）。讨论了解释和实际后果。
Diffusion processes with small noise conditioned to reach a target set are considered. The AMS algorithm is a Monte Carlo method that is used to sample such rare events by iteratively simulating clones of the process and selecting trajectories that have reached the highest value of a so-called importance function. In this paper, the large sample size relative variance of the AMS small probability estimator is considered. The main result is a large deviations logarithmic equivalent of the latter in the small noise asymptotics, which is rigorously derived. It is given as a maximisation problem explicit in terms of the quasi-potential cost function associated with the underlying small noise large deviations. Necessary and sufficient geometric conditions ensuring the vanishing of the obtained quantity ('weak' asymptotic efficiency) are provided. Interpretations and practical consequences are discussed.
