An introduction to probabilistic methods with applications

Pierre Del Moral; Nicolas G. Hadjiconstantinou

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 44, Issue: 5, page 805-829
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Del Moral, Pierre, and Hadjiconstantinou, Nicolas G.. "An introduction to probabilistic methods with applications." ESAIM: Mathematical Modelling and Numerical Analysis 44.5 (2010): 805-829. <http://eudml.org/doc/250775>.

@article{DelMoral2010,
abstract = { 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. },
author = {Del Moral, Pierre, Hadjiconstantinou, Nicolas G.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
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},
language = {eng},
month = {8},
number = {5},
pages = {805-829},
publisher = {EDP Sciences},
title = {An introduction to probabilistic methods with applications},
url = {http://eudml.org/doc/250775},
volume = {44},
year = {2010},
}

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
DA - 2010/8//
PB - EDP Sciences
VL - 44
IS - 5
SP - 805
EP - 829
AB - 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.
LA - eng
KW - 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
UR - http://eudml.org/doc/250775
ER -

References

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