Radial processes on RCD (K,N) spaces

Kazumasa Kuwada, Kazuhrio Kuwae

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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 languageEnglish
Pages (from-to)72-108
Number of pages37
JournalJournal des Mathematiques Pures et Appliquees
Volume126
DOIs
Publication statusPublished - 2019 Jun

Keywords

  • Alexandrov space
  • Dirichlet form
  • Laplacian comparison theorem
  • RCD (K,N)-space
  • Radial process
  • Riemannian manifold

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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