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.
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.