Tree based functional expansions for Feynman--Kac particle models

DOI10.1214/08-AAP565zbMath1189.60171arXiv0906.4249OpenAlexW2952964321MaRDI QIDQ1024905

Sylvain Rubenthaler, Pierre Del Moral, Frédéric Patras

Publication date: 17 June 2009

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.4249

zbMATH Keywords

automorphism groupscombinatorial enumerationinteracting particle systemsFeynman-Kac semigroupstrees and forests

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Population dynamics (general) (92D25) Combinatorial probability (60C05) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80) Integral representations, integral operators, integral equations methods in higher dimensions (31B10) Schrödinger and Feynman-Kac semigroups (47D08) Stochastic particle methods (65C35)

Related Items (12)

Central limit theorem through expansion of the propagation of chaos for Bird and Nanbu systems ⋮ Stability properties of some particle filters ⋮ A sharp first order analysis of Feynman-Kac particle models. I: Propagation of chaos ⋮ A central limit theorem for conservative fragmentation chains ⋮ Linear variance bounds for particle approximations of time-homogeneous Feynman-Kac formulae ⋮ Convergence of \(U\)-statistics for interacting particle systems ⋮ \(U\)-statistics of Ornstein-Uhlenbeck branching particle system ⋮ A second order analysis of McKean-Vlasov semigroups ⋮ A nonasymptotic theorem for unnormalized Feynman-Kac particle models ⋮ On the stability of sequential Monte Carlo methods in high dimensions ⋮ Bias behaviour and antithetic sampling in mean-field particle approximations of SDEs nonlinear in the sense of McKean ⋮ The Convergence to Equilibrium of Neutral Genetic Models

Cites Work

• Trees, renormalization and differential equations.
• Renormalization in quantum field theory and the Riemann-Hilbert problem. I: The Hopf algebra structure of graphs and the main theorem
• Sequential Monte Carlo Methods in Practice
• Renormalization
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