Feynman-Kac Formulae

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.