Convergence of Non-Symmetric Diffusion Processes on RCD spaces

TL;DR

This paper constructs and analyzes non-symmetric diffusion processes on RCD spaces, exploring their conservativeness and convergence properties using non-smooth differential structures.

Contribution

It introduces a method to construct non-symmetric diffusions on RCD spaces utilizing non-smooth differential structures, and studies their convergence behavior.

Findings

Constructed non-symmetric diffusions on RCD spaces.

Analyzed conservativeness of the diffusion processes.

Established weak convergence results related to geometric convergence.

Abstract

We construct non-symmetric diffusion processes associated with Dirichlet forms consisting of uniformly elliptic forms and derivation operators with killing terms on RCD spaces by aid of non-smooth differential structures introduced by Gigli '16. After constructing diffusions, we investigate conservativeness and the weak convergence of the laws of diffusions in terms of a geometric convergence of the underling spaces and convergences of the corresponding coefficients.