This special volume of the ESAIM Journal, Mathematical Modelling and Numerical Analysis,
contains a collection of articles on probabilistic interpretations of
some classes of nonlinear integro-differential equations.
The selected contributions deal with a wide range of topics in applied probability theory and stochastic analysis,
with applications in a variety of scientific disciplines, including
physics, biology, fluid
mechanics, molecular chemistry, financial mathematics and bayesian statistics. In this preface, we provide a
brief presentation of the main contributions presented in this special volume. We have also included
an introduction to classic probabilistic methods and a presentation of the more recent particle methods, with a synthetic picture of their mathematical foundations and their range of applications.