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Feynman-Kac Formulae

Genealogical and Interacting Particle Systems with Applications

  • Pierre Del Moral

Part of the Probability and its Applications book series (PIA)

Table of contents

  1. Front Matter
    Pages i-xviii
  2. Pierre Del Moral
    Pages 1-45
  3. Pierre Del Moral
    Pages 47-93
  4. Pierre Del Moral
    Pages 95-119
  5. Pierre Del Moral
    Pages 121-155
  6. Pierre Del Moral
    Pages 157-186
  7. Pierre Del Moral
    Pages 187-214
  8. Pierre Del Moral
    Pages 215-251
  9. Pierre Del Moral
    Pages 253-289
  10. Pierre Del Moral
    Pages 291-330
  11. Pierre Del Moral
    Pages 331-386
  12. Pierre Del Moral
    Pages 387-426
  13. Pierre Del Moral
    Pages 427-522
  14. Back Matter
    Pages 523-557

About this book

Introduction

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-Schrödinger 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 Probabilités of Paul Sabatier University in Toulouse. He received his Ph.D. in signal processing at the LAAS-CNRS (Laboratoire d'Analyse et Architecture des Systèmes) 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.

Keywords

Feynman-Kac formula Markov chain Markov kernel Markov process Monte Carlo method Statistical Physics algorithms filtering problem genetic algorithms interacting particle system

Authors and affiliations

  • Pierre Del Moral
    • 1
  1. 1.Laboratoire de Statistique et ProbabilitésUniversité Paul SabatierToulouse, Cedex 4France

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-9393-1
  • Copyright Information Springer-Verlag New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-1902-1
  • Online ISBN 978-1-4684-9393-1
  • Series Print ISSN 1431-7028
  • Buy this book on publisher's site