Del Moral Pierre


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Research Book

Feynman-Kac Formulae
Genealogical and Interacting Particle Systems with Applications

(Springer New York; Springer Heidelberg, Series: Probability and its Applications)
(also available at Amazon fr, us, ca. )

  • Mathematical analysis:: 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, large deviations principles for strong topologies on path-distribution spaces.

  • Applications: Spectral analysis of Feynman-Kac-Schrodinger operators, Dirichlet problems with boundary conditions, finance, molecular analysis, rare events and directed polymers simulation, genetic algorithms, Metropolis-Hasting type models, filtering problems and hidden Markov chains.

  • Particle models: Branching and interacting particle systems, path space and excursion space particle models, ancestral and descendant genealogical tree models.

  • 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.