Construction of diffusion processes on fractals, \(d\)-sets, and general metric measure spaces. (English) Zbl 1086.60052
Summary: We give a sufficient condition to construct non-trivial \(\mu\)-symmetric diffusion processes on a locally compact separable metric measure space \((M,\rho,\mu)\). These processes are associated with local regular Dirichlet forms which are obtained as contiuous parts of \(\Gamma\)-limits for approximating nonlocal Dirichlet forms. For various fractals we can use existing estimates to verify our assumptions. This shows that our general method of constructing diffusions can be applied to these fractals.
MSC:
60J60 | Diffusion processes |
49Q20 | Variational problems in a geometric measure-theoretic setting |
60J35 | Transition functions, generators and resolvents |