Feynman-Kac公式的后向粒子解释
A Backward Particle Interpretation of Feynman-Kac Formulae
摘要：
我们设计了一个粒子解释的费曼-卡茨措施道路空间的基础上，结合传统的平均场粒子解释的流动，其最终的时间边缘的向后马尔可夫表示。与传统的基于谱系树的模型相比，这些新的粒子算法可以用于计算归一化的加性泛函“在运行中”，以及它们的限制占用措施，具有给定的精度，不依赖于最终的时间范围。我们提供了w.r.t.的一致收敛性结果。时间范围参数以及泛函中心极限定理和指数浓度估计。我们还说明了这些结果的背景下，计算物理和虚时薛定谔型偏微分方程，特别感兴趣的数值逼近的不变测度相关的$h$ -过程。
英文摘要：
We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results w.r.t. the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. We also illustrate these results in the context of computational physics and imaginary time Schroedinger type partial differential equations, with a special interest in the numerical approximation of the invariant measure associated to $h$-processes.
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