Mean-field particle methods
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Mean field particle methods are a broad class interacting type Monte Carlo algorithms for simulating from a sequence of probability distributions satisfying a nonlinear evolution equation. These probabilistic models can always be interpreted as the law of a Markov process whose random evolution depends on the distributions of its random states. A natural way to simulate these complex nonlinear Markov processes is to sample a large number of copies of the process and to replace in their evolution equation the unknown distributions of the random states by the sampled empirical measures. In contrast with traditional Monte Carlo methodologies these mean field particle techniques rely on sequentially interacting samples.
In physics, and more particularly in statistical mechanics, these nonlinear evolution equations are often used to describe the statistical behavior of microscopic interacting particles in a fluid or in some condensed matter. In this context, the resulting nonlinear Markov processes are mainly presented by McKean Vlasov processes or Boltzmann type collision processes.