How to construct diffusion processes on metric spaces (Q1387638)

Let \((X,d)\) be a locally compact metric space and \(m\) a positive Radon measure on \(X\). Using the theory of Dirichlet forms the author presents a very nice general method to construct \(m\)-symmetric diffusion processes on \(X\). In the special case where \(X\) is a Riemannian manifold and \(d\) the Riemannian distance, the \(m\)-symmetric diffusion obtained is just Brownian motion on \(X\). Though these diffusions are always associated with a local Dirichlet form, they are constructed as \(\Gamma\)-limits of approximating nonlocal Dirichlet forms.