Volume 44, Number 5, September-October 2010Special Issue on Probabilistic methods and their applications
|Page(s)||805 - 829|
|Published online||26 August 2010|
An introduction to probabilistic methods with applications
Centre INRIA Bordeaux et Sud-Ouest & Institut de
Mathématiques de Bordeaux, Université de Bordeaux I, 351 cours de la Libération,
33405 Talence Cedex, France. Pierre.Del-Moral@inria.fr
2 Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge MA 02139-4307, USA. email@example.com
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.
Mathematics Subject Classification: 65M75 / 68Q87 / 60H35 / 35Q68 / 37N10 / 35Q35 / 35Q20
Key words: 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
© EDP Sciences, SMAI, 2010
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