Genealogical particle analysis of rare events
Genealogical particle analysis of rare events
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DOI：
10.1214/105051605000000566
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发表时间：
2005-11-01
影响因子：
1.8
通讯作者：
Garnier, J
中科院分区：
文献类型：
--
作者：
del Moral, P;Garnier, J
在本文中，开发了一种原始的相互作用粒子系统方法，用于研究罕见事件状态下的马尔可夫链。所提出的粒子系统通过 Feynman-Kac 路径测量的谱系树解释进行了理论上的研究。给出了粒子系统的算法实现。提出了罕见事件发生概率的估计器并计算其方差，从而可以比较和优化算法的不同版本。讨论了应用和数值实现。首先，我们将粒子系统技术应用于玩具模型（高斯随机游走），这可以说明理论预测。其次，我们解决了一个物理相关问题，即估计光纤中偏振模色散引起的中断概率。
In this paper an original interacting particle system approach is developed for studying Markov chains in rare event regimes. The proposed particle system is theoretically studied through a genealogical tree interpretation of Feynman-Kac path measures. The algorithmic implementation of the particle system is presented. An estimator for the probability of occurrence of a rare event is proposed and its variance is computed, which allows to compare and to optimize different versions of the algorithm. Applications and numerical implementations are discussed. First, we apply the particle system technique to a toy model (a Gaussian random walk), which permits to illustrate the theoretical predictions. Second, we address a physically relevant problem consisting in the estimation of the outage probability due to polarization-mode dispersion in optical fibers.