# 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

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topDel 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 -

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