Finite-particle approximations for interacting Brownian particles with logarithmic potentials
Finite-particle approximations for interacting Brownian particles with logarithmic potentials
We prove the convergence of $N$-particle systems of Brownian particles with logarithmic interaction potentials onto a system described by the infinite-dimensional stochastic differential equation (ISDE). For this proof we present two general theorems on the finite-particle approximations of interacting Brownian motions. In the first general theorem, we present a sufficient …