A nonasymptotic theorem for unnormalized Feynman-Kac particle models
A nonasymptotic theorem for unnormalized Feynman-Kac particle models
复制标题
非归一化 Feynman-Kac 粒子模型的非渐近定理
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
A. Guyader
中科院分区：
文献类型：
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作者：
F. Cérou;P. Moral;A. Guyader
给出了非规格化Feynman-Kac模型的相互作用粒子逼近的一个非渐近定理。我们提供了一种基于Feynman-Kac半群技术的原始随机分析，结合了最近开发的基于聚结树的粒子块分布函数表示。我们提出了一些规则性条件，在这些条件下，这些加权粒子测量的L(2)相对误差相对于时间范围线性增长，产生了这类非标准化模型的第一个此类结果。我们还在粒子吸收模型的背景下说明了这些结果，对罕见事件分析特别感兴趣。
We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman-Kac models. We provide an original stochastic analysis-based on Feynman-Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the L(2)-relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first results of this type for this class of unnormalized models. We also illustrate these results in the context of particle absorption models, with a special interest in rare event analysis.