An introduction to probabilistic methods with applications
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 5, p. 805-829

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.

DOI : https://doi.org/10.1051/m2an/2010043
Classification:  65M75,  68Q87,  60H35,  35Q68,  37N10,  35Q35,  35Q20
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
@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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {44},
number = {5},
year = {2010},
pages = {805-829},
doi = {10.1051/m2an/2010043},
mrnumber = {2731394},
language = {en},
url = {http://www.numdam.org/item/M2AN_2010__44_5_805_0}
}

Del Moral, Pierre; Hadjiconstantinou, Nicolas G. An introduction to probabilistic methods with applications. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 44 (2010) no. 5, pp. 805-829. doi : 10.1051/m2an/2010043. http://www.numdam.org/item/M2AN_2010__44_5_805_0/

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