Convergence of Non-Symmetric Diffusion Processes on RCD spaces
arXiv:1709.09536 · doi:10.1007/s00526-018-1398-7
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.
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 modified
References in corpus (4)
- Well posedness of Lagrangian flows and continuity equations in metric measure spaces
- On quotients of spaces with Ricci curvature bounded below
- Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
- Convergence of Brownian Motions on Metric Measure Spaces Under Riemannian Curvature-Dimension Conditions