Authors construct strong solutions to ISDEs for Coulomb interacting Brownian motions in d ≥ 2 and β > 0, proving pathwise uniqueness and showing the dynamics arise as limits of finite-particle approximations via reflecting domains and N-particle systems.
RIMS Kokyuroku Bessatsu, B59 [Series of Lecture Notes from RIMS], Research Institute for Mathematical Sciences (RIMS), Kyoto, 2016
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Infinite-dimensional stochastic differential equations for Coulomb random point fields
Authors construct strong solutions to ISDEs for Coulomb interacting Brownian motions in d ≥ 2 and β > 0, proving pathwise uniqueness and showing the dynamics arise as limits of finite-particle approximations via reflecting domains and N-particle systems.