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

Classification : 65M75,  68Q87,  60H35,  35Q68,  37N10,  35Q35,  35Q20
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
     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},
     pages = {805--829},
     publisher = {EDP-Sciences},
     volume = {44},
     number = {5},
     year = {2010},
     doi = {10.1051/m2an/2010043},
     mrnumber = {2731394},
     language = {en},
     url = {}
AU  - Del Moral, Pierre
AU  - Hadjiconstantinou, Nicolas G.
TI  - An introduction to probabilistic methods with applications
JO  - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY  - 2010
DA  - 2010///
SP  - 805
EP  - 829
VL  - 44
IS  - 5
PB  - EDP-Sciences
UR  -
UR  -
UR  -
DO  - 10.1051/m2an/2010043
LA  - en
ID  - M2AN_2010__44_5_805_0
ER  - 
Del Moral, Pierre; Hadjiconstantinou, Nicolas G. An introduction to probabilistic methods with applications. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 44 (2010) no. 5, pp. 805-829. doi : 10.1051/m2an/2010043.

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