An introduction to probabilistic methods with applications

Pierre Del Moral; Nicolas G. Hadjiconstantinou

Displaying similar documents to “An introduction to probabilistic methods with applications”

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...

Branching and interacting particle systems. Approximations of Feynman-Kac formulae with applications to non-linear filtering

Pierre Del Moral, Laurent Miclo (2000)

Séminaire de probabilités de Strasbourg

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Standard stochastic coalescence with sum kernels.

Fournier, Nicolas (2006)

Electronic Communications in Probability [electronic only]

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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 and spatial limit theorems for lattice and continuum particle systems.

Penrose, Mathew D. (2008)

Probability Surveys [electronic only]

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A stochastic cobweb dynamical model.

Brianzoni, Serena, Mammana, Cristiana, Michetti, Elisabetta, Zirilli, Francesco (2008)

Discrete Dynamics in Nature and Society

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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....

A nonasymptotic theorem for unnormalized Feynman–Kac particle models

F. Cérou, P. Del Moral, A. Guyader (2011)

Annales de l'I.H.P. Probabilités et statistiques

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We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to...