Abstract
In this paper, we show a stochastic expression for the radial processes of Brownian motions on RCD ⁎ (K,N)-spaces. It corresponds to the one on Riemannian manifolds. The expression holds for all starting points without exceptional sets. It can be extended beyond the hitting time to the reference point provided the reference point is sufficiently regular. We further prove that the regularity condition is satisfied for almost every reference point. Our results extend the comparison theorems over Alexandrov spaces proved in [36,29].
Original language | English |
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Pages (from-to) | 72-108 |
Number of pages | 37 |
Journal | Journal des Mathematiques Pures et Appliquees |
Volume | 126 |
DOIs | |
Publication status | Published - 2019 Jun |
Externally published | Yes |
Keywords
- Alexandrov space
- Dirichlet form
- Laplacian comparison theorem
- RCD (K,N)-space
- Radial process
- Riemannian manifold
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics