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August 2020 Hydrodynamic limit and propagation of chaos for Brownian particles reflecting from a Newtonian barrier
Clayton L. Barnes
Ann. Appl. Probab. 30(4): 1582-1613 (August 2020). DOI: 10.1214/19-AAP1536

Abstract

In 2001, Frank Knight constructed a stochastic process modeling the one-dimensional interaction of two particles, one being Newtonian in the sense that it obeys Newton’s laws of motion, and the other particle being Brownian. We construct a multi-particle analog, using Skorohod map estimates in proving a propagation of chaos, and characterizing the hydrodynamic limit as the solution to a PDE with free boundary condition. This PDE resembles the Stefan problem but has a Neumann type boundary condition. Stochastic methods are used to show existence and uniqueness for this free boundary problem.

Citation

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Clayton L. Barnes. "Hydrodynamic limit and propagation of chaos for Brownian particles reflecting from a Newtonian barrier." Ann. Appl. Probab. 30 (4) 1582 - 1613, August 2020. https://doi.org/10.1214/19-AAP1536

Information

Received: 1 February 2018; Revised: 1 September 2019; Published: August 2020
First available in Project Euclid: 4 August 2020

MathSciNet: MR4132635
Digital Object Identifier: 10.1214/19-AAP1536

Subjects:
Primary: 60, 60K35
Secondary: 60J55, 82

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.30 • No. 4 • August 2020
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