Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

This paper focuses on interacting particle systems methods for solving numerically a class of Feynman-Kac formulae arising in the study of certain parabolic differential equations, physics, biology, evolutionary computing, nonlinear filtering and elsewhere. We have tried to give an “expose” of the mathematical theory that is useful for analyzing the convergence of such genetic-type and particle approximating models including law of large numbers, large deviations principles, fluctuations and empirical process theory as well as semigroup techniques and limit theorems for processes.

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