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Feynman-Kac Formulae : Genealogical and Interacting Particle Systems with Applications - Pierre Del Moral

Feynman-Kac Formulae

Genealogical and Interacting Particle Systems with Applications

Hardcover

Published: 1st March 2004
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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. Topics include spectral analysis of Feynman-Kac-Schrodinger operators, Dirichlet problems with boundary conditions, finance, molecular analysis, rare events and directed polymers simulation, genetic algorithms, Metropolis-Hastings type models, as well as filtering problems and hidden Markov chains.

This text takes readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of non-linear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagations of chaos, central limit, and Berry Esseen type theorems as well as large deviations principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods and worked out illustrations of the key aspect of the theory.

With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research who have a background in probability and Markov chain theory.

From the reviews:

"I also recommend this book as informal reading for anyone intersted in the subject, preferably with a strong background in Markov processes; in particular, for someone also familiar with one of the many fields to which the book applies Feynman-Kac models. The book is entertaining and informative." Journal of the American Statistical Association, December 2005

From the reviews:

"I also recommend this book as informal reading for anyone intersted in the subject, preferably with a strong background in Markov processes; in particular, for someone also familiar with one of the many fields to which the book applies Feynman-Kac models. The book is entertaining and informative." Journal of the American Statistical Association, December 2005

"This book takes the readers in a clear and progressive format from simple to recent and advanced topics in pure and applied probability. ... With practical and easy to use references, as well as deeper and modern mathematics studies, the book will be of use to engineers and researchers in pure and applied mathematics. Also researches in statistics, physics, biology, and operation research who have a background of Probability and Markov chain theory, can benefit from the monograph." (Lucien Lemmens, Physicalia, Vol. 57 (3), 2005)

"Pierre Del Moral has produced an extraordinary research and reference book which will be of great use to a large and diverse scientific and engineering community. The book deals in detail with convergence theorems for and applications of so-called Feynman-Kac models and their interacting particle representations. ... The book's main contribution is twofold ... provides excellent models amenable to particle approximation. Del Moral is best known for his research ... . The book contains many references to this branch of his work." (Mathematical Reviews, 2005)

"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. ... 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." (Jie Xiong, Zentralblatt MATH, Vol. 1130 (8), 2008)

Introduction
Feynman-Kac Formulae
Genealogical and Interacting Particle Models
Stability of Feynman-Kac Semi-groups
Invariant Measures and Related Topics
Annealing Properties
Asymptotic Behavior
Propagations of Chaos
Central Limit Theorems
Large Deviations Principles
Feynman-Kac and Interacting Particle Recipes
Applications
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780387202686
ISBN-10: 0387202684
Series: Probability and Its Applications
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 556
Published: 1st March 2004
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 22.9 x 15.2  x 3.18
Weight (kg): 1.1