Diffusion processes and heat kernels on metric spaces
Diffusion processes and heat kernels on metric spaces
We present a general method to construct $m$-symmetric diffusion processes $(X_t, \mathbf{P}_x)$ on any given locally compact metric space $(X, d)$ equipped with a Radon measure $m$. These processes are associated with local regular Dirichlet forms which are obtained as $\Gamma$-limits of approximating nonlocal Dirichlet forms. This general method works …