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

R. Eymard, M. Roussignol and A. Tordeux

Stochastic Processes and their Applications, 2012, vol. 122, issue 11, 3648-3679

Abstract: 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.

Keywords: Misanthrope stochastic process; Non linear scalar hyperbolic equation; Entropy Young measure solution; Traffic flow simulation; Weak BV inequality (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spa.2012.07.002

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