Displaying similar documents to “Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation”

Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process

Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We study a free energy computation procedure, introduced in [Darve and Pohorille, (2001) 9169–9183; Hénin and Chipot, (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre , (2008)...

Quantitative concentration inequalities on sample path space for mean field interaction

François Bolley (2010)

ESAIM: Probability and Statistics

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We consider the approximation of a mean field stochastic process by a large interacting particle system. We derive non-asymptotic large deviation bounds measuring the concentration of the empirical measure of the paths of the particles around the law of the process. The method is based on a coupling argument, strong integrability estimates on the paths in Hölder norm, and a general concentration result for the empirical measure of identically distributed independent paths. ...

An introduction to probabilistic methods with applications

Pierre Del Moral, Nicolas G. Hadjiconstantinou (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This special volume of the ESAIM Journal, , 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...

Stochastic Lagrangian method for downscaling problems in computational fluid dynamics

Frédéric Bernardin, Mireille Bossy, Claire Chauvin, Jean-François Jabir, Antoine Rousseau (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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This work aims at introducing modelling, theoretical and numerical studies related to a new downscaling technique applied to computational fluid dynamics. Our method consists in building a local model, forced by large scale information computed thanks to a classical numerical weather predictor. The local model, compatible with the Navier-Stokes equations, is used for the small scale computation (downscaling) of the considered fluid. It is inspired by Pope's works on turbulence, and...

Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups

Pierre Del Moral, L. Miclo (2003)

ESAIM: Probability and Statistics

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We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of N interacting particles evolving in an environment with soft obstacles related to a potential function V . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique....