Feynman-Kac Formulae

Abstract

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 from simple to recent and advanced topics in pure and applied probability such as contraction and annealed properties of nonlinear semi-groups, functional entropy inequalities, empirical process convergence, increasing propagation 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 illustration of the key aspect of the theory." "With 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."--Jacket. 1. Introduction -- 2. Feynman-Kac formulae -- 3. Genealogical and interacting particle models -- 4. Stability of Feynman-Kac semigroups -- 5. Invariant measures and related topics -- 6. Annealing properties -- 7. Asymptotic behavior -- 8. Propagation of chaos -- 9. Central limit theorems -- 10. Large-deviation principles -- 11. Feynman-Kac and interacting particle recipes -- 12. Applications.