Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds

Suzuki, Kohei

Abstract

The Sobolev regularity of invariant measures for diffusion processes is proved on non-smooth metric measure spaces with synthetic lower Ricci curvature bounds. As an application, the symmetrizability of semigroups is characterized, and the stability of invariant measures is proved under perturbations of drifts and the underlying spaces in the sense of the measured Gromov convergence.

Citation

Suzuki, K. (2022). Regularity and stability of invariant measures for diffusion processes under synthetic lower Ricci curvature bounds. Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, XXIII(2), 745-808. https://doi.org/10.2422/2036-2145.201911_001

• Journal Article Type: Article
• Acceptance Date: Feb 3, 2021
• Publication Date: Jun 23, 2022
• Deposit Date: Oct 20, 2024
• Journal: Annali della Scuola Normale Superiore di Pisa, Classe di Scienze
• Print ISSN: 0391-173X
• Electronic ISSN: 2036-2145
• Publisher: Scuola Normale Superiore - Edizioni della Normale
• Peer Reviewed: Peer Reviewed
• Volume: XXIII
• Issue: 2
• Pages: 745-808
• DOI: https://doi.org/10.2422/2036-2145.201911_001
• Public URL: https://durham-repository.worktribe.com/output/2977803