Convergence of Non-Symmetric Diffusion Processes on RCD spaces

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.Comment: 41 pages. To appear in Calc. Var. PDEs. In the second version, the following have been modified: Section 2.3, 2.4, 2.5, 2.6 were added. Assumption 3.3, Proposition 3.4, Remark 3.5, and Example 3.7 were deleted. Example 7.2 was replaced with Corollary 7.2. Theorem 4.4 was modifie