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Article Dans Une Revue Stochastic Processes and their Applications Année : 2012

Convergence of a misanthrope process to the entropy solution of 1D problems

Résumé

We prove the convergence, in some strong sense, of a Markov process called "a misanthrope process" to the entropy weak solution of a one-dimensional scalar nonlinear hyperbolic equation. Such a process may be used for the simulation of traffic flows. The convergence proof relies on the uniqueness of entropy Young measure solutions to the nonlinear hyperbolic equation, which holds for both the bounded and the unbounded cases. In the unbounded case, we also prove an error estimate. Finally, numerical results show how this convergence result may be understood in practical cases.
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Dates et versions

hal-00623832 , version 1 (15-09-2011)

Identifiants

Citer

Robert Eymard, Michel Roussignol, Antoine Tordeux. Convergence of a misanthrope process to the entropy solution of 1D problems. Stochastic Processes and their Applications, 2012, 122, http://www.sciencedirect.com/science/article/pii/S0304414912001536. ⟨10.1016/j.spa.2012.07.002⟩. ⟨hal-00623832⟩
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