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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.
Keywords: 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
Del Moral, Pierre; Hadjiconstantinou, Nicolas G. An introduction to probabilistic methods with applications. ESAIM: Mathematical Modelling and Numerical Analysis , Special Issue on Probabilistic methods and their applications, Tome 44 (2010) no. 5, pp. 805-829. doi: 10.1051/m2an/2010043
@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: Mathematical Modelling and Numerical Analysis },
pages = {805--829},
year = {2010},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
doi = {10.1051/m2an/2010043},
mrnumber = {2731394},
language = {en},
url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis PY - 2010 SP - 805 EP - 829 VL - 44 IS - 5 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis %D 2010 %P 805-829 %V 44 %N 5 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an/2010043/ %R 10.1051/m2an/2010043 %G en %F M2AN_2010__44_5_805_0
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