This monograph presents some new concentration inequalities for Feynman-Kac particle processes.

It analyzes different types of stochastic particle models, including particle profile occupation

measures, genealogical tree based evolution models, particle free energies, as well as

backward Markov chain particle models. It illustrates these results with a series of topics related

to computational physics and biology, stochastic optimization, signal processing and Bayesian

statistics, and many other probabilistic machine learning algorithms. Special emphasis is given

to the stochastic modeling, and to the quantitative performance analysis of a series of advanced

Monte Carlo methods; including particle filters, genetic type island models, Markov bridge

models, and interacting particle Markov chain Monte Carlo methodologies.