Super-Brownian motion with reflecting historical paths. II: Convergence of approximations

Abstract

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "super-Brownian motion with reflecting historical paths." This solves an open problem posed in [?], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [?] for all subsequential limits—they obviously hold for the unique limit found in the present paper.