TREE BASED FUNCTIONAL EXPANSIONS FOR FEYNMAN-KAC PARTICLE MODELS

被引：13
作者：
Del Moral, Pierre [1 ,2 ]
Patras, Frederic [3 ]
Rubenthaler, Sylvain [3 ]
机构：
[1] Univ Bordeaux 1, CNRS, UMR 5251, Ctr INRIA Bordeaux Sud Ouest, F-33405 Talence, France
[2] Univ Bordeaux 1, CNRS, UMR 5251, Inst Math Bordeaux, F-33405 Talence, France
[3] Univ Nice Sophia Antipolis, Lab JA Dieudonne, UMR 6621, CNRS, F-06108 Nice 02, France
来源：
ANNALS OF APPLIED PROBABILITY | 2009年 / 19卷 / 02期
关键词：
Feynman-Kac semigroups; interacting particle systems; trees and forests; automorphism groups; combinatorial enumeration; RENORMALIZATION;
D O I：
10.1214/08-AAP565
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We design exact polynomial expansions of a class of Feynman-Kac particle distributions. These expansions are finite and are parametrized by coalescent trees and other related combinatorial quantities. The accuracy of the expansions at any order is related naturally to the number of coalescences of the trees. Our results include an extension of the Wick product formula to interacting particle systems. They also provide refined nonasymptotic propagation of chaos-type properties, as well as sharp L-p-mean error bounds, and laws of large numbers for U-statistics.
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页码：778 / 825
页数：48
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