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Displaying similar documents to “Particle approximations of Lyapunov exponents connected to Schrödinger operators and Feynman–Kac semigroups”

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...

Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation

François Bolley, Arnaud Guillin, Florent Malrieu (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation ...

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)...