This book presents the first comprehensive and modern mathematical treatment of these mean field particle models, including refined convergence analysis on nonlinear Markov chain models. It also covers applications related to parameter estimation in hidden Markov chain models, stochastic optimization, nonlinear filtering and multiple target tracking, stochastic optimization, calibration and uncertainty propagations in numerical codes, rare event simulation, financial mathematics, and free energy and quasi-invariant measures arising in computational physics and population biology.
Autorentext
Pierre Del Moral is a professor in the School of Mathematics and Statistics at the University of New South Wales in Sydney, Australia.
Zusammenfassung
In the last three decades, there has been a dramatic increase in the use of interacting particle methods as a powerful tool in real-world applications of Monte Carlo simulation in computational physics, population biology, computer sciences, and statistical machine learning. Ideally suited to parallel and distributed computation, these advanced par
Inhalt
Monte Carlo and Mean Field Models. Theory and Applications. Feynman-Kac Models: Discrete Time Feynman-Kac Models. Four Equivalent Particle Interpretations. Continuous Time Feynman-Kac Models. Nonlinear Evolutions of Intensity Measures. Application Domains: Particle Absorption Models. Signal Processing and Control Systems. Theoretical Aspects: Mean Field Feynman-Kac Models. A General Class of Mean Field Models. Empirical Processes. Feynman-Kac Semigroups. Intensity Measure Semigroups. Particle Density Profiles. Genealogical Tree Models. Particle Normalizing Constants. Backward Particle Markov Models. Bibliography. Index.