Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models
Genealogies and Increasing Propagation of Chaos For Feynman-Kac and Genetic Models
复制标题
Feynman-Kac 和遗传模型的谱系和混沌传播的增加
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
L. Miclo
中科院分区：
文献类型：
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作者：
P. Moral;L. Miclo
提出了一种用于描述遗传算法谱系结构的路径值交互粒子系统模型。我们把整个祖先树的历史过程和分布与路空间上的一类Feynman-Kac公式联系起来。我们还证明了增加和uniforversions的传播混沌适当的粒子块的大小和时间范围产生什么似乎是第一个结果，这类粒子系统的这种类型。1.导论.在过去的二十年里，围绕着遗传算法和费曼-卡茨公式之间的联系，它们取得了重要的进展。这门学科与生物学、进化计算、物理学和高级信号处理有着天然的联系。希望了解更多关于这些连接和具体应用的详细信息的读者，建议查阅调查文件[8]和其中的参考文献。在前面引用的论文中，我们主要讨论了当粒子数趋于无穷大时，与遗传型粒子系统相关的经验测度的渐近行为。这里提出的强版本的混沌传播提供了几个措施的中心性和渐近独立的一块粒子的分布到一个给定的时间范围。这些渐近结果补充和加强了[8]中的结果。本工作的另一个侧面主题涉及群体遗传学历史过程的建模和收敛分析。除了固有的和数学的兴趣，研究遗传算法的谱系结构的一个实际原因是，这种设置正是我们需要解决的数值，所谓的非线性滤波和平滑问题.这一开头部分被分解为三个部分。我们开始在1.1节从Feynman-Kac公式开始，并提供相应的遗传型相互作用粒子系统近似模型的简要描述。在第1.2节中，我们详细描述了本文的主要结果。在第1.3节中，我们对该主题的相关工作和一些悬而未决的问题进行了一些评论。这里有一些标准的符号，在所有的文件中使用。�系我� �
A path-valued interacting particle systems model for the genealogical structure of genetic algorithms is presented. We connect the historical process and the distribution of the whole ancestral tree with a class of Feynman-Kac formulae on path space. We also prove increasing and uniformversions of propagation of chaos for appropriate particle block size and time horizon yielding what seems to be the first result of this type for this class of particle systems. 1. Introduction. Over the last two decades themhave been im portant developments centering around the connections between genetic algorithms and Feynman-Kac formulae. This subject has natural links to biology, evolutionary computing, physics and advanced signal processing. The reader who wishes to know more details about these connections and specific applications is recommended to consult the survey paper [8] and references therein. In the previously referenced paper we essentially discussed the asymptotic behavior of the empirical measures associated to genetic-type particle systems as the number of particles tends to infinity. The strong versions of propagation of chaos presented here provide several measures of centrality and asymptotic independence for the distribution of a block of particles up to a given time horizon. These asymptotic results complement and strengthen those presented in [8]. Another side topic of the present work concerns the modeling and the convergence analysis of the historical process in population genetics. Aside from inherent and mathematical interest one of the practical reasons for studying the genealogical structure of a genetic algorithmstems fromthe fact that this set up is precisely what we need to solve numerically the so-called non linear filtering and smoothing problem. This opening section is decomposed into three parts. We begin in Section 1.1 with the Feynman-Kac formulae and provide a brief description of the corresponding genetic-type interacting particle system approximating model. In Section 1.2 we describe in some details the main results of the paper. In Section 1.3 we close with some comments on related works on the subject and some open problems. Here are some standard notations to be used in all the paper. Let � � E� �