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Journal of Dynamics and Differential Equations

, Volume 30, Issue 4, pp 1661–1682 | Cite as

Non-local Conservation Law from Stochastic Particle Systems

  • Marielle Simon
  • Christian OliveraEmail author
Article
  • 148 Downloads

Abstract

We consider an interacting particle system in \(\mathbb {R}^d\) modelled as a system of N stochastic differential equations. The limiting behaviour as the size N grows to infinity is achieved as a law of large numbers for the empirical density process associated with the interacting particle system.

Keywords

Stochastic differential equations Fractal conservation law Lévy process Particle systems Semi-group approach 

Mathematics Subject Classification

60H20 60H10 60F99 

Notes

Acknowledgements

C.O. is partially supported by CNPq through the Grant 460713/2014-0 and FAPESP by the Grants 2015/04723-2 and 2015/07278-0. This work benefited from the support of the Project EDNHS ANR-14-CE25-0011 of the French National Research Agency (ANR). The work of M.S. was also supported by the Labex CEMPI (ANR-11-LABX-0007-01).

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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.MEPHYSTO TeamINRIA Lille - Nord EuropeVilleneuve-d’AscqFrance
  2. 2.Laboratoire Paul Painlevé, CNRS UMRVilleneuve-d’AscqFrance
  3. 3.Departamento de MatemáticaUniversidade Estadual de CampinasCampinasBrazil

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