2017/10/31 by Clayton Barnes
Economics, Econometrics and Finance · Mathematics · #Boundary (topology) #Boundary value problem #Brownian motion #Classical mechanics #Limit (mathematics) #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematics #Newtonian fluid #Particle system #Physics #Statistical physics #Stochastic process #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Uniqueness #math.PR #msc:60 #msc:60J55 #msc:60K35 #msc:82
paper · pdf · doi:10.1214/19-aap1536
44 pages, 1 figure
openalex created_date 2017/11/10 · arxiv created 2020/01/29 · openalex publication_date 2020/08/01 · arxiv updated 2021/02/18 · openalex updated_date 2026/08/05
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.