AN INTRODUCTION TO PROBABILISTIC METHODS WITH APPLICATIONS

被引：2

作者：

Del Moral, Pierre ^{[1
,3
]}

Hadjiconstantinou, Nicolas G. ^{[2
]}

机构：

[1] Univ Bordeaux 1, Ctr INRIA Bordeaux & Sud Ouest, F-33405 Talence, France

[2] MIT, Cambridge, MA 02139 USA

[3] Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2010年 / 44卷 / 05期

关键词：

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; PARTICLE APPROXIMATION; CONVERGENCE; INEQUALITIES; EQUILIBRIUM; STABILITY; EQUATIONS;

D O I：

10.1051/m2an/2010043

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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 integrodifferential 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.

引用

页码：805 / 829

页数：25

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