| Issue |
ESAIM: M2AN
Volume 44, Number 5, September-October 2010
Special Issue on Probabilistic methods and their applications
|
|
|---|---|---|
| Page(s) | 805 - 829 | |
| DOI | https://doi.org/10.1051/m2an/2010043 | |
| Published online | 26 August 2010 | |
An introduction to probabilistic methods with applications
1
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. ngh@mit.edu
Received:
2
January
2009
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
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.