Genealogical and Interacting Particle Systems with Applications.
Springer, New York; Series: Probability and Applications 2004 (at Amazon fr, us, ca)
Pierre Del Moral
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 of Probability and Markov chain theory.
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Horizon Maths, Les maths se devoilent aux industriels; Fondation Science Maths de Paris, Tour AREVA, dec. 2011.
(programme)
( lecture notes (in french))
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Sino-French Summer Institute 2011.Beijing, China, June 13-25, 2011.
((lecture note 1), (lecture note 2), and (lecture note 3))
- INRIA Workshop on Statistical Learning Institut Henri Poincaré Paris, December 5-6, 2011 ( (lecture notes) )
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University of Cambridge, Statistics Laboratory seminar, Feb. 2010.
(lecture notes)
- 10th Machine Learning summer school, September 1-15th, 2008. (lecture notes)
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Opening workshop, Sequential Monte Carlo Methods, SAMSI, Duke Univ. September 7-10th, 2008.
(lecture notes)
- Pierre Del Moral, Peng Hu, Liming Wu
On the concentration properties of Interacting particle processes
HAL-INRIA RR-7677 (2011), To appear in Foundations and Trends in Machine Learning (160p.) (2011-2012).
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Del Moral P., Miclo L.
Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering.
Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor, Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).
More information:
Preface
Contents
References
Corrections/improvements
Selected slides : (see also Conference lecture notes)
Some complementary studies
Links to some application model areas
Filtering, Advanced Signal Processing
Biology, Chemistry
Rare events analysis
Applied Probability and Physics
Equivalent Monte Carlo models: Sequential Monte Carlo Methods, Particle Filters, Genetic Algorithms, Evolutionary Population models, Population Monte Carlo methods, Diffusion Monte Carlo and Quantum Monte Carlo models, spawning filters, cloning algorithms, pruning and enrichment models, go with the winner, replenish strategies, and many others.
Lectures notes (in french) with a collection Scilab programs
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