Construction of Diffusion Processes

The duality between the Brownian motion and Laplacian on \$\mathbb{R}^d\$ illustrates a quite intricate link between diffusion processes (continuous Markov processes) and local symmetric bilinear forms. In this talk, we will go through some standard methods to construct the standard Brownian motion and see how they inspire us to construct diffusion processes in more general settings. If time permits, we will also briefly talk about how to make diffusions on manifolds explicitly using standard Brownian motions. The talk is expository and no advanced knowledge of probability, spectral theory or potential theory will be assumed.