Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions

Kohei Suzuki

Published 2017-03-21Version 1

We show that the pointed measured Gromov convergence of the underlying spaces implies (or under some condition, is equivalent to) the weak convergence of Brownian motions under Riemannian Curvature-Dimension (RCD) conditions. This paper is an improved and jointed version of the previous two manuscripts arXiv:1509.02025 and arXiv:1603.08622. The improvements extend our results to the case of sigma-finite reference measures and to the case that initial distributions of Brownian motions are possible to be dirac measures.