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.
Mots clés : Fokker-Planck equations, Vlasov diffusion models, fluid-lagrangian-velocities model, Boltzmann collision models, interacting jump processes, adaptive biasing force model, molecular dynamics, ground state energies, hidden Markov chain problems, Feynman-Kac semigroups, Dirichlet problems with boundary conditions, Poisson Boltzmann equations, mean field stochastic particle models, stochastic analysis, functional contraction inequalities, uniform propagation of chaos properties w.r.t. the time parameter
@article{M2AN_2010__44_5_805_0,
author = {Del Moral, Pierre and Hadjiconstantinou, Nicolas G.},
title = {An introduction to probabilistic methods with applications},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {805--829},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
year = {2010},
doi = {10.1051/m2an/2010043},
mrnumber = {2731394},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an/2010043/}
}
TY - JOUR AU - Del Moral, Pierre AU - Hadjiconstantinou, Nicolas G. TI - An introduction to probabilistic methods with applications JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2010 SP - 805 EP - 829 VL - 44 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an/2010043/ DO - 10.1051/m2an/2010043 LA - en ID - M2AN_2010__44_5_805_0 ER -
%0 Journal Article %A Del Moral, Pierre %A Hadjiconstantinou, Nicolas G. %T An introduction to probabilistic methods with applications %J ESAIM: Modélisation mathématique et analyse numérique %D 2010 %P 805-829 %V 44 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an/2010043/ %R 10.1051/m2an/2010043 %G en %F M2AN_2010__44_5_805_0
Del Moral, Pierre; Hadjiconstantinou, Nicolas G. An introduction to probabilistic methods with applications. ESAIM: Modélisation mathématique et analyse numérique, Tome 44 (2010) no. 5, pp. 805-829. doi : 10.1051/m2an/2010043. http://archive.numdam.org/articles/10.1051/m2an/2010043/
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