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 particle algorithms include nonlinear interacting jump diffusions; quantum, diffusion, and resampled Monte Carlo methods; Feynman-Kac particle models; genetic and evolutionary algorithms; sequential Monte Carlo methods; adaptive and interacting Markov chain Monte Carlo models; bootstrapping methods; ensemble Kalman filters; and interacting particle filters. Mean Field Simulation for Monte Carlo Integration presents the first comprehensive and modern mathematical treatment of mean field particle simulation models and interdisciplinary research topics, including interacting jumps and McKean-Vlasov processes, sequential Monte Carlo methodologies, genetic particle algorithms, genealogical tree-based algorithms, and quantum and diffusion Monte Carlo methods. Along with covering refined convergence analysis on nonlinear Markov chain models, the author discusses 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. This book shows how mean field particle simulation has revolutionized the field of Monte Carlo integration and stochastic algorithms. It will help theoretical probability researchers, applied statisticians, biologists, statistical physicists, and computer scientists work better across their own disciplinary boundaries.
Monte Carlo and Mean Field Models Linear evolution equations Nonlinear McKean evolutions Time discretization schemes Illustrative examples Mean field particle methods Theory and Applications A stochastic perturbation analysis Feynman-Kac particle models Extended Feynman-Kac models Nonlinear intensity measure equations Statistical machine learning models Risk analysis and rare event simulation Feynman-Kac Models Discrete Time Feynman-Kac Models A brief treatise on evolution operators Feynman-Kac models Some illustrations Historical processes Feynman-Kac sensitivity measures Four Equivalent Particle Interpretations Spatial branching models Sequential Monte Carlo methodology Interacting Markov chain Monte Carlo algorithms Mean field interacting particle models Continuous Time Feynman-Kac Models Some operator aspects of Markov processes Feynman-Kac models Continuous time McKean models Mean field particle models Nonlinear Evolutions of Intensity Measures Intensity of spatial branching processes Nonlinear equations of positive measures Multiple-object nonlinear filtering equations Association tree-based measures Application Domains Particle Absorption Models Particle motions in absorbing medium Mean field particle models Some illustrations Absorption models in random environments Particle Feynman-Kac models Doob h-processes Signal Processing and Control Systems Nonlinear filtering problems Linear Gaussian models Interacting Kalman filters Quenched and annealed filtering models Particle quenched and annealed models Parameter estimation in hidden Markov models Optimal stopping problems Theoretical Aspects Mean Field Feynman-Kac Models Feynman-Kac models McKean-Markov chain models Perfect sampling models Interacting particle systems Some convergence estimates Continuous time models A General Class of Mean Field Models Description of the models Some weak regularity properties Some illustrative examples A stochastic coupling technique Fluctuation analysis Empirical Processes Description of the models Nonasymptotic theorems A reminder on Orlicz's norms Finite marginal inequalities Maximal inequalities Cramer-Chernov inequalities Perturbation analysis Interacting processes Feynman-Kac Semigroups Description of the models Stability properties Semigroups of nonlinear Markov chain models Backward Markovian semigroups Intensity Measure Semigroups Spatial branching models Measure-valued nonlinear equations Weak Lipschitz properties of semigroups Stability properties of PHD models Particle Density Profiles Stochastic perturbation analysis First order expansions Some nonasymptotic theorems Fluctuation analysis Concentration inequalities A general class of mean field particle models Particle branching intensity measures Positive measure particle equations Genealogical Tree Models Some equivalence principles Some nonasymptotic theorems Ancestral tree occupation measures Central limit theorems Concentration inequalities Particle Normalizing Constants Unnormalized particle measures Some key decompositions Fluctuation theorems A nonasymptotic variance theorem Lp-mean error estimates Concentration analysis Backward Particle Markov Models Description of the models Conditioning principles Integral transport properties Additive functional models A stochastic perturbation analysis Orlicz norm and Lm-mean error estimates Some nonasymptotic variance estimates Fluctuation analysis Concentration inequalities Bibliography Index
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