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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

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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.

DOI : 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 
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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

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