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

Author: Pierre Moral
Publisher: New York, NY : Springer New York, 2004.
Series: Probability and its Applications, A Series of the Applied Probability Trust.
Edition/Format:   eBook : Bibliographic data : EnglishView all editions and formats
Database:WorldCat
Summary:
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-Schrdinger operators, Dirichlet problems with boundary conditions, finance, molecular analysis,  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Printed edition:
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Pierre Moral
ISBN: 9781468493931 1468493930 9781441919021 1441919023
OCLC Number: 840289979
Description: 1 online resource (XVIII, 555 pages 15 illustrations).
Contents: 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.
Series Title: Probability and its Applications, A Series of the Applied Probability Trust.
Responsibility: by Pierre Moral.

Abstract:

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-Schrdinger 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. Pierre Del Moral is a research fellow in mathematics at the C.N.R.S. (Centre National de la Recherche Scientifique) at the Laboratoire de Statistique et Probabilits of Paul Sabatier University in Toulouse. He received his Ph. D. in signal processing at the LAAS-CNRS (Laboratoire d'Analyse et Architecture des Systmes) of Toulouse. He is one of the principal designers of the modern and recently developing theory on particle methods in filtering theory. He served as a research engineer in the company Steria-Digilog from 1992 to 1995 and he has been a visiting professor at Purdue University and Princeton University. He is a former associate editor of the journal Stochastic Analysis and Applications.

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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 Read more...

 
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