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Mean Field Limit for Stochastic Particle Systems

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Active Particles, Volume 1

Abstract

We review some classical and more recent results for the derivation of mean field equations from systems of many particles, focusing on the stochastic case where a large system of SDEs leads to a McKean–Vlasov PDE as the number N of particles goes to infinity. Classical mean field limit results require that the interaction kernel be essentially Lipschitz. To handle more singular interaction kernels is a long-standing and challenging question but which has had some recent successes.

P-E Jabin is partially supported by NSF Grant 1312142 and by NSF Grant RNMS (Ki-Net) 1107444.

Z. Wang is supported by NSF Grant 1312142.

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Authors and Affiliations

  1. CSCAMM and Dept. of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Pierre-Emmanuel Jabin & Zhenfu Wang

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  1. Pierre-Emmanuel Jabin
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  2. Zhenfu Wang
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Correspondence to Pierre-Emmanuel Jabin .

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Editors and Affiliations

  1. Department of Mathematical Sciences, King Abdulaziz University, Jeddah, Saudi Arabia

    Nicola Bellomo

  2. Department of Mathematics, Imperial College London, London, United Kingdom

    Pierre Degond

  3. CSCAMM, University of Maryland, College Park, USA

    Eitan Tadmor

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Jabin, PE., Wang, Z. (2017). Mean Field Limit for Stochastic Particle Systems. In: Bellomo, N., Degond, P., Tadmor, E. (eds) Active Particles, Volume 1 . Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-49996-3_10

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