The talk will concentrate on applications of Dirichlet boundary problems in metric measure spaces to limit laws of stochastic processes in such spaces. This is a companion to the talk on spectrum, regularity and $L^{p}$-estimates of eigenfunctions, as well as irreducibility of the corresponding killed stochastic processes. The limit laws include small deviations, large time behavior of the heat content, Chung's LIL and finding the Onsager-Machlup functional.