Construction of diffusion processes on fractals, d-sets, and general metric measure spaces

Abstract

We give a sufficient condition to construct non-trivial /j-symmetric diffusion processes on a locally compact separable metric measure space (A[,p,μ). These processes are associated with local regular Dirichlet forms which are obtained as continuous parts of P-limits for approximating non-local 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.