Brownian Motion and the Dirichlet Problem
In this Bachelor's thesis, a solution to the Dirichlet problem using Brownian motion is given. Brownian motion is constructed using Kolmogorov's existence and continuity theorems. Blumenthal's zero-one law and the strong Markov property in various formulations are proven. Using these results, a solution to the Dirichlet problem is given using Brownian motion. The cone condition which g
