Feynman-Kac formulae: genealogical and interacting particle systems with applications / Pierre Del Moral

Auteur: Del Moral, Pierre (1965-) - AuteurType de document: Livre numérique Collection: Probability and its applications Langue: anglaisÉditeur: Berlin : Springer, cop. 2004 ISBN: 9780387202686 Note: Examples in engineering science, Bayesian methodology, particle and statistical physics, biology, and applied probability and statistics are given to motivate the study of the Feynman-Kac models in this book. It is demonstrated that the Feynman-Kac and particle model is one of the most active contact point among these fields of applications. This book provides a unifying treatment for the topics mentioned above whose areas of research were developing independently. This book can serve as the textbook for an entire course on Feynman-Kac Formulae and particle system approximation. It can also serve as a main reference for courses on topics like stochastic filtering, mathematical models for population genetics, mathematical biology, etc. The first chapter provides an overview of the book. In chapter 2, a rigorous mathematical description of the Feynman-Kac models with an emphasis on path-valued processes is given. Chapter 3 is devoted to interacting particle approximation. Various qualitative properties (stability, invariant measure, and long time limit) are studied in chapters 4–6. Convergence of the particle approximation is investigated in chapters 7–10 when the number of particles in the system tends to infinity. The methods of evaluating the rate of convergence include central limit theorem and large deviation principle. Finally, chapters 11 and 12 are concerned with the applications of the Feynman-Kac modelling and the particle methodology developed in this book (zbMath) Sujets MSC: 60H30 Probability theory and stochastic processes -- Stochastic analysis -- Applications of stochastic analysis (to PDE, etc.)
60K35 Probability theory and stochastic processes -- Special processes -- Interacting random processes; statistical mechanics type models; percolation theory
82C22 Statistical mechanics, structure of matter -- Time-dependent statistical mechanics (dynamic and nonequilibrium) -- Interacting particle systems
82C80 Statistical mechanics, structure of matter -- Time-dependent statistical mechanics (dynamic and nonequilibrium) -- Numerical methods (Monte Carlo, series resummation, etc.)
92D25 Biology and other natural sciences -- Genetics and population dynamics -- Population dynamics (general)
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Examples in engineering science, Bayesian methodology, particle and statistical physics, biology, and applied probability and statistics are given to motivate the study of the Feynman-Kac models in this book. It is demonstrated that the Feynman-Kac and particle model is one of the most active contact point among these fields of applications. This book provides a unifying treatment for the topics mentioned above whose areas of research were developing independently. This book can serve as the textbook for an entire course on Feynman-Kac Formulae and particle system approximation. It can also serve as a main reference for courses on topics like stochastic filtering, mathematical models for population genetics, mathematical biology, etc. The first chapter provides an overview of the book. In chapter 2, a rigorous mathematical description of the Feynman-Kac models with an emphasis on path-valued processes is given. Chapter 3 is devoted to interacting particle approximation. Various qualitative properties (stability, invariant measure, and long time limit) are studied in chapters 4–6. Convergence of the particle approximation is investigated in chapters 7–10 when the number of particles in the system tends to infinity. The methods of evaluating the rate of convergence include central limit theorem and large deviation principle. Finally, chapters 11 and 12 are concerned with the applications of the Feynman-Kac modelling and the particle methodology developed in this book (zbMath)

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