An Introduction to probabilistic methods, with applications.

Pierre del Moral (1) , Hadjiconstantinou Nicolas G. (2)

1 ALEA - Advanced Learning Evolutionary Algorithms
2 MIT - Massachusetts Institute of Technology

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.

Domaines: Probabilités [math.PR]

Pierre del Moral, Hadjiconstantinou Nicolas G.. An Introduction to probabilistic methods, with applications.. ESAIM: Mathematical Modelling and Numerical Analysis, 2010, Special Issue on Probabilistic methods and their applications, 44, pp.805 - 829. ⟨10.1051/m2an/2010043⟩. ⟨inria-00533434⟩