Convergence of Brownian motions on RCD(K,infty) spaces

2016/03/29 by Kohei SUZUKI, Suzuki, Kohei
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Mathematical Dynamics and Fractals #Primary 60F17 #Probability (math.PR) #Secondary 53C23 #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1603.08622

openalex publication_date 2016/03/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Suppose that metric measure spaces X_n=(X_n, d_n, m_n) satisfy RCD(K,infty) conditions with m_n(X_n)=1. Then the measured Gromov convergence (introduced by Gigili-Mondino-Savare '13) of X_n is equivalent to the weak convergence of the laws of Brownian motions on X_n with initial distributions m_n.

Citations

• Metric measure spaces with Riemannian Ricci curvature bounded from below
• Local Poincaré inequalities from stable curvature conditions on metric spaces
• Collapsing of Riemannian manifolds and eigenvalues of Laplace operator

Related

• Convergence of Brownian motions on RCD*(K,N) spaces
• Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions
• Metric Measure Spaces with Variable Ricci Bounds and Couplings of Brownian Motions
• Limiting behaviors of the Brownian motions on hyperbolic spaces
• Chernoff's Theorem and Discrete Time Approximations of Brownian Motion on Manifolds