Displaying similar documents to “Steady state and scaling limit for a traffic congestion model”

Brownian particles with electrostatic repulsion on the circle: Dyson's model for unitary random matrices revisited

Emmanuel Cépa, Dominique Lépingle (2010)

ESAIM: Probability and Statistics

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The Brownian motion model introduced by Dyson [7] for the eigenvalues of unitary random matrices is interpreted as a system of interacting Brownian particles on the circle with electrostatic inter-particles repulsion. The aim of this paper is to define the finite particle system in a general setting including collisions between particles. Then, we study the behaviour of this system when the number of particles goes to infinity (through the empirical measure process). We prove...

Simulation and approximation of Lévy-driven stochastic differential equations

Nicolas Fournier (2012)

ESAIM: Probability and Statistics

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We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like ||d near , for some (1,2), we obtain an error of order 1/√ with a computational cost of order . For a similar error when...