| Summary: | Interacting particle methods are increasingly used to sample from complex
high-dimensional distributions. They have found a wide range of applications in applied
probability, Bayesian statistics and information engineering. Understanding rigorously
these new Monte Carlo simulation tools leads to fascinating mathematics related to
Feynman-Kac path integral theory and their interacting particle interpretations. In these
lecture notes, we provide a pedagogical introduction to the stochastic modeling and the
theoretical analysis of these particle algorithms. We also illustrate these methods
through several applications including random walk confinements, particle absorption
models, nonlinear filtering, stochastic optimization, combinatorial counting and directed
polymer models.
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