Feynman-Kac Formulae

Genealogical and Interacting Particle Systems with Applications
Softcover Nachdruck of the original 1. Auflage 2004
ISBN: 978-1-4419-1902-1
Verlag: Springer

Buch, Englisch, 556 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 861 g

Reihe: Probability and Its Applications

This book contains a systematic and self-contained treatment of Feynman-Kac path measures, their genealogical and interacting particle interpretations, and their applications to a variety of problems arising in statistical physics, biology, and advanced engineering sciences. With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to advanced undergraduates as well as to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research.

Zielgruppe

Research

Autoren/Hrsg.

Del Moral, Pierre

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme

Inhaltsverzeichnis

1 Introduction.- 1.1 On the Origins of Feynman-Kac and Particle Models.- 1.2 Notation and Conventions.- 1.3 Feynman-Kac Path Models.- 1.4 Motivating Examples.- 1.5 Interacting Particle Systems.- 1.6 Sequential Monte Carlo Methodology.- 1.7 Particle Interpretations.- 1.8 A Contents Guide for the Reader.- 2 Feynman-Kac Formulae.- 2.1 Introduction.- 2.2 An Introduction to Markov Chains.- 2.4 Structural Stability Properties.- 2.5 Distribution Flows Models.- 2.6 Feynman-Kac Models in Random Media.- 2.7 Feynman-Kac Semigroups.- 3 Genealogical and Interacting Particle Models.- 3.1 Introduction.- 3.2 Interacting Particle Interpretations.- 3.3 Particle models with Degenerate Potential.- 3.4 Historical and Genealogical Tree Models.- 3.5 Particle Approximation Measures.- 4 Stability of Feynman-Kac Semigroups.- 4.1 Introduction.- 4.2 Contraction Properties of Markov Kernels.- 4.3 Contraction Properties of Feynman-Kac Semigroups.- 4.4 Updated Feynman-Kac Models.- 5 Invariant Measures and Related Topics.- 5.1 Introduction.- 5.2 Existence and Uniqueness.- 5.3 Invariant Measures and Feynman-Kac Modeling.- 5.4 Feynman-Kac and Metropolis-Hastings Models.- 5.5 Feynman-Kac-Metropolis Models.- 6 Annealing Properties.- 6.1 Introduction.- 6.2 Feynman-Kac-Metropolis Models.- 6.3 Feynman-Kac Trapping Models.- 7 Asymptotic Behavior.- 7.1 Introduction.- 7.2 Some Preliminaries.- 7.3 Inequalities for Independent Random Variables.- 7.4 Strong Law of Large Numbers.- 8 Propagation of Chaos.- 8.1 Introduction.- 8.2 Some Preliminaries.- 8.3 Outline of Results.- 8.4 Weak Propagation of Chaos.- 8.5 Relative Entropy Estimates.- 8.6 A Combinatorial Transport Equation.- 8.7 Asymptotic Properties of Boltzmann-Gibbs Distributions.- 8.8 Feynman-Kac Semigroups.- 9 Central Limit Theorems.- 9.1 Introduction.- 9.2Some Preliminaries.- 9.3 Some Local Fluctuation Results.- 9.4 Particle Density Profiles.- 9.5 A Berry-Esseen Type Theorem.- 9.6 A Donsker Type Theorem.- 9.7 Path-Space Models.- 9.8 Covariance Functions.- 10 Large-Deviation Principles.- 10.1 Introduction.- 10.2 Some Preliminary Results.- 10.3 Crámer’s Method.- 10.4 Laplace-Varadhan’s Integral Techniques.- 10.5 Dawson-Gärtner Projective Limits Techniques.- 10.6 Sanov’s Theorem.- 10.7 Path-Space and Interacting Particle Models.- 10.8 Particle Density Profile Models.- 11 Feynman-Kac and Interacting Particle Recipes.- 11.1 Introduction.- 11.2 Interacting Metropolis Models.- 11.3 An Overview of some General Principles.- 11.4 Descendant and Ancestral Genealogies.- 11.5 Conditional Explorations.- 11.6 State-Space Enlargements and Path-Particle Models.- 11.7 Conditional Excursion Particle Models.- 11.8 Branching Selection Variants.- 11.9 Exercises.- 12 Applications.- 12.1 Introduction.- 12.2 Random Excursion Models.- 12.3 Change of Reference Measures.- 12.4 Spectral Analysis of Feynman-Kac-Schrödinger Semigroups.- 12.5 Directed Polymers Simulation.- 12.6 Filtering/Smoothing and Path estimation.- References.