Introduction.- Feynman-Kac Formulae.- Genealogical and Interacting Particle Models.- Stability of Feynman-Kac Semi-groups.- Invariant Measures and Related Topics.- Annealing Properties.- Asymptotic Behavior.- Propagations of Chaos.- Central Limit Theorems.- Large Deviations Principles.- Feynman-Kac and Interacting Particle Recipes.- Applications.
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 deviation principles for strong topologies on path-distribution spaces. Topics also include a body of powerful branching and interacting particle methods.
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. With practical and easy to use references as well as deeper and modern mathematics studies, the book will be of use to advanced undergraduates as well as to engineers and researchers in pure and applied mathematics, statistics, physics, biology, and operation research.